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301. A steel ball of radius $2 \, \text{mm}$ is dropped in oil of viscosity $0.6 \, \text{Pa·s}$. If densities of steel and oil are $7800 \, \text{kg/m}^3$ and $900 \, \text{kg/m}^3$, calculate its terminal velocity. ($ g = 9.8 \, \text{m/s}^2$)
ⓐ. 0.10 m/s
ⓑ. 0.15 m/s
ⓒ. 0.20 m/s
ⓓ. 0.25 m/s
Correct Answer: 0.15 m/s
Explanation: $v_t = \frac{2 r^2 g (\rho_s – \rho_f)}{9 \eta}$.
Substitute: $r = 0.002, \Delta \rho = 6900, g = 9.8, \eta = 0.6$.
$v_t = \frac{2 (0.002^2)(9.8)(6900)}{9(0.6)} \approx 0.15 \, m/s$.
302. A raindrop of radius $0.5 \, mm$ falls through air ($ \eta = 1.8 \times 10^{-5} \, Pa·s$, $\rho_{air} = 1.2 \, kg/m^3$). If water density is $1000 \, kg/m^3$, find its terminal velocity.
ⓐ. 3 m/s
ⓑ. 5 m/s
ⓒ. 7 m/s
ⓓ. 9 m/s
Correct Answer: 7 m/s
Explanation: $v_t = \frac{2 r^2 g (\rho_s – \rho_f)}{9 \eta}$.
$r = 5 \times 10^{-4}, \Delta \rho = 998.8, g = 9.8, \eta = 1.8 \times 10^{-5}$.
Result: $v_t \approx 7 \, m/s$.
303. A small ball of radius $0.001 \, m$ has a terminal velocity of $0.02 \, m/s$ in a liquid of viscosity $0.4 \, Pa·s$. If density of liquid = $1200 \, kg/m^3$, calculate density of the ball.
ⓐ. 1250 $kg/m^3$
ⓑ. 1300 $kg/m^3$
ⓒ. 1400 $kg/m^3$
ⓓ. 1500 $kg/m^3$
Correct Answer: 1400 $kg/m^3$
Explanation: $v_t = \frac{2 r^2 g (\rho_s – \rho_f)}{9 \eta}$.
Rearrange: $\rho_s = \rho_f + \frac{9 \eta v_t}{2 r^2 g}$.
Substitute values: $\rho_s = 1200 + \frac{9 (0.4)(0.02)}{2 (10^{-6})(9.8)} \approx 1400 \, kg/m^3$.
304. A lead sphere of radius $1.5 \, mm$ is falling in glycerin of viscosity $1.5 \, Pa·s$. If lead density = $11300 \, kg/m^3$ and glycerin density = $1260 \, kg/m^3$, find terminal velocity.
ⓐ. 0.10 m/s
ⓑ. 0.15 m/s
ⓒ. 0.20 m/s
ⓓ. 0.25 m/s
Correct Answer: 0.10 m/s
Explanation: $v_t = \frac{2 (0.0015^2)(9.8)(10040)}{9 (1.5)} \approx 0.10 \, m/s$.
305. A pollen grain of radius $2 \times 10^{-6} \, m$ is falling in air ($ \eta = 1.8 \times 10^{-5} \, Pa·s, \rho_{air} = 1.2 \, kg/m^3$). If density of pollen = $900 \, kg/m^3$, calculate terminal velocity.
ⓐ. $1.2 \times 10^{-6} \, m/s$
ⓑ. $2.0 \times 10^{-6} \, m/s$
ⓒ. $3.0 \times 10^{-6} \, m/s$
ⓓ. $4.0 \times 10^{-6} \, m/s$
Correct Answer: $2.0 \times 10^{-6} \, m/s$
Explanation: Using $v_t = \frac{2 r^2 g (\rho_s – \rho_f)}{9 \eta}$.
Substitute: $r = 2 \times 10^{-6}, \Delta \rho = 898.8, g = 9.8$.
$v_t \approx 2.0 \times 10^{-6} \, m/s$.
306. A ball of radius $3 \, mm$ falls through oil of viscosity $0.7 \, Pa·s$ with density difference $2000 \, kg/m^3$. Calculate terminal velocity.
ⓐ. 0.05 m/s
ⓑ. 0.10 m/s
ⓒ. 0.20 m/s
ⓓ. 0.30 m/s
Correct Answer: 0.30 m/s
Explanation: $v_t = \frac{2 r^2 g \Delta \rho}{9 \eta} = \frac{2 (0.003^2)(9.8)(2000)}{9 (0.7)} \approx 0.30 \, m/s$.
307. A small sphere of radius $0.0005 \, m$ falls in a liquid of viscosity $0.25 \, Pa·s$. If terminal velocity is $0.015 \, m/s$ and density of liquid = $1000 \, kg/m^3$, calculate density of the sphere.
ⓐ. 1100 $kg/m^3$
ⓑ. 1200 $kg/m^3$
ⓒ. 1250 $kg/m^3$
ⓓ. 1300 $kg/m^3$
Correct Answer: 1200 $kg/m^3$
Explanation: $\rho_s = \rho_f + \frac{9 \eta v}{2 r^2 g}$.
Substitute: $\rho_s = 1000 + \frac{9 (0.25)(0.015)}{2 (2.5 \times 10^{-7})(9.8)} \approx 1200 \, kg/m^3$.
308. A steel ball of radius $0.004 \, m$ falls in oil of viscosity $0.8 \, Pa·s$. If density difference is $7000 \, kg/m^3$, calculate its terminal velocity.
ⓐ. 0.25 m/s
ⓑ. 0.50 m/s
ⓒ. 0.75 m/s
ⓓ. 1.0 m/s
Correct Answer: 0.50 m/s
Explanation: $v_t = \frac{2 r^2 g \Delta \rho}{9 \eta} = \frac{2 (0.004^2)(9.8)(7000)}{9 (0.8)} \approx 0.50 \, m/s$.
309. A ball of radius $0.001 \, m$ falls in glycerin ($ \eta = 1.0 \, Pa·s$, $\rho_f = 1260 \, kg/m^3$). If terminal velocity is found to be $0.015 \, m/s$, calculate the density of the ball.
ⓐ. 1400 $kg/m^3$
ⓑ. 1500 $kg/m^3$
ⓒ. 1600 $kg/m^3$
ⓓ. 1700 $kg/m^3$
Correct Answer: 1600 $kg/m^3$
Explanation: $\rho_s = \rho_f + \frac{9 \eta v}{2 r^2 g}$.
Substitute: $\rho_s = 1260 + \frac{9 (1)(0.015)}{2 (10^{-6})(9.8)} \approx 1600 \, kg/m^3$.
310. A particle of radius $0.002 \, m$ falls in a fluid of viscosity $0.2 \, Pa·s$. If density difference = $1000 \, kg/m^3$, calculate its terminal velocity.
ⓐ. 0.004 m/s
ⓑ. 0.008 m/s
ⓒ. 0.009 m/s
ⓓ. 0.010 m/s
Correct Answer: 0.008 m/s
Explanation: $v_t = \frac{2 r^2 g \Delta \rho}{9 \eta} = \frac{2 (0.002^2)(9.8)(1000)}{9 (0.2)} \approx 0.008 \, m/s$.
311. A streamline in fluid flow is defined as:
ⓐ. The path along which a dust particle moves in air
ⓑ. A line tangent to the velocity of the fluid at every point
ⓒ. A line perpendicular to the velocity vector
ⓓ. A path along which pressure remains constant
Correct Answer: A line tangent to the velocity of the fluid at every point
Explanation: A streamline represents the direction of fluid velocity at every point. Fluid elements do not cross streamlines.
312. Which of the following is a characteristic of streamline (laminar) flow?
ⓐ. Fluid layers mix randomly
ⓑ. Flow velocity is the same at all points
ⓒ. Fluid particles move in parallel layers without crossing
ⓓ. Flow is always turbulent
Correct Answer: Fluid particles move in parallel layers without crossing
Explanation: In laminar flow, fluid moves smoothly in parallel layers with no mixing between them, unlike in turbulence.
313. In turbulent flow:
ⓐ. Fluid particles follow fixed paths
ⓑ. Pressure and velocity fluctuate irregularly
ⓒ. Energy loss is negligible
ⓓ. Viscosity has no role
Correct Answer: Pressure and velocity fluctuate irregularly
Explanation: Turbulent flow is chaotic, with random mixing, irregular eddies, and fluctuating velocity and pressure fields.
314. Which of the following examples best demonstrates laminar flow?
ⓐ. Smoke rising smoothly from a candle flame
ⓑ. Water gushing from a broken dam
ⓒ. Airflow around a fast airplane wing
ⓓ. Flood waters in a river
Correct Answer: Smoke rising smoothly from a candle flame
Explanation: When smoke rises slowly, it forms smooth streamlines (laminar flow). At higher velocity, it becomes turbulent.
315. Which of the following examples best demonstrates turbulent flow?
ⓐ. Oil flowing slowly in a thin capillary tube
ⓑ. Water flowing slowly in a narrow pipe
ⓒ. River water flowing rapidly over rocks
ⓓ. Blood flow in small capillaries
Correct Answer: River water flowing rapidly over rocks
Explanation: Turbulent flow occurs at high velocity and large Reynolds number, such as in river rapids with chaotic swirls.
316. Which statement is true about streamline flow?
ⓐ. It occurs at high Reynolds number
ⓑ. Energy losses are minimum
ⓒ. Velocity distribution is always uniform
ⓓ. Streamlines cross each other frequently
Correct Answer: Energy losses are minimum
Explanation: Laminar flow has ordered motion with minimal energy dissipation compared to turbulent flow.
317. When smoke rising from incense sticks changes from smooth to irregular, it indicates transition from:
ⓐ. Vacuum to turbulence
ⓑ. Streamline to turbulent flow
ⓒ. High to low pressure
ⓓ. Ideal fluid to viscous fluid
Correct Answer: Streamline to turbulent flow
Explanation: Initially, smoke rises smoothly in layers (laminar), but at higher velocity it breaks into eddies, showing turbulence.
318. In streamline flow, the velocity at a point is:
ⓐ. Constant with time
ⓑ. May change with time but direction is random
ⓒ. Different for each particle at the same point
ⓓ. Independent of pressure
Correct Answer: Constant with time
Explanation: In steady (laminar) flow, velocity of fluid at a given point remains constant with time.
319. Which of the following factors increases the chance of turbulent flow?
ⓐ. Low velocity, small diameter, high viscosity
ⓑ. High velocity, large diameter, low viscosity
ⓒ. Low velocity, narrow pipe, high viscosity
ⓓ. High viscosity, low velocity
Correct Answer: High velocity, large diameter, low viscosity
Explanation: Turbulence is more likely when fluid speed and pipe diameter are large, and viscosity is low, corresponding to high Reynolds number.
320. Which of the following is NOT a feature of turbulent flow?
ⓐ. Formation of eddies
ⓑ. Random mixing of fluid layers
ⓒ. Smooth and orderly particle motion
ⓓ. High energy losses
Correct Answer: Smooth and orderly particle motion
Explanation: Smooth and orderly motion is a property of laminar (streamline) flow, not turbulent flow. Turbulent flow is irregular and energy-dissipative.
321. The Reynolds experiment demonstrates:
ⓐ. Verification of Pascal’s law
ⓑ. Verification of Archimedes’ principle
ⓒ. Transition between laminar and turbulent flow in fluids
ⓓ. Measurement of buoyant force
Correct Answer: Transition between laminar and turbulent flow in fluids
Explanation: Osborne Reynolds’ experiment used a dye filament in flowing water through a glass tube to show laminar, transitional, and turbulent flow depending on flow velocity.
322. In Reynolds’ experiment, the flow is laminar when the dye filament:
ⓐ. Spreads out randomly in the tube
ⓑ. Breaks into eddies
ⓒ. Remains a straight line along the tube
ⓓ. Moves perpendicular to water flow
Correct Answer: Remains a straight line along the tube
Explanation: In laminar flow, the dye moves in a straight, smooth path along the flow direction without mixing.
323. The dimensionless number introduced by Osborne Reynolds to predict flow regime is called:
ⓐ. Mach number
ⓑ. Reynolds number
ⓒ. Weber number
ⓓ. Froude number
Correct Answer: Reynolds number
Explanation: Reynolds number ($Re$) is a dimensionless parameter predicting whether flow is laminar, transitional, or turbulent.
324. The Reynolds number is defined as:
ⓐ. $Re = \frac{\eta v}{\rho L}$
ⓑ. $Re = \frac{\rho v L}{\eta}$
ⓒ. $Re = \frac{v}{\rho \eta L}$
ⓓ. $Re = \frac{\rho g h}{\eta}$
Correct Answer: $Re = \frac{\rho v L}{\eta}$
Explanation: Reynolds number is the ratio of inertial force to viscous force. It depends on density ($\rho$), velocity ($v$), characteristic length ($L$), and viscosity ($\eta$).
325. In Reynolds’ experiment, the flow becomes turbulent when Reynolds number:
ⓐ. $Re < 2000$
ⓑ. $Re > 4000$
ⓒ. $Re \approx 1$
ⓓ. $Re < 100$
Correct Answer: $Re > 4000$
Explanation: Critical Reynolds number for transition: laminar flow occurs for $Re < 2000$, turbulent for $Re > 4000$, and 2000–4000 is transitional.
326. In Reynolds’ experiment, transitional flow occurs in the range of Reynolds number:
ⓐ. 0–100
ⓑ. 200–500
ⓒ. 2000–4000
ⓓ. Above 10,000
Correct Answer: 2000–4000
Explanation: Transitional flow regime exists between laminar ($<2000$) and turbulent ($>4000$) flow.
327. Reynolds number is a ratio of:
ⓐ. Gravitational force to viscous force
ⓑ. Inertial force to viscous force
ⓒ. Buoyant force to viscous force
ⓓ. Pressure force to surface tension force
Correct Answer: Inertial force to viscous force
Explanation: Reynolds number compares the relative importance of inertial forces to viscous forces in fluid flow, predicting laminar or turbulent conditions.
328. If Reynolds number is less than 2000, the flow is:
ⓐ. Laminar
ⓑ. Transitional
ⓒ. Turbulent
ⓓ. Not possible
Correct Answer: Laminar
Explanation: Laminar flow regime is observed for $Re < 2000$, where viscous forces dominate and flow is smooth.
329. Which parameter does NOT directly affect Reynolds number?
ⓐ. Velocity of fluid
ⓑ. Characteristic length (pipe diameter)
ⓒ. Fluid density
ⓓ. Gravitational acceleration
Correct Answer: Gravitational acceleration
Explanation: Reynolds number depends on velocity, density, viscosity, and characteristic length, but not directly on gravity.
330. Osborne Reynolds used what fluid in his famous experiment?
ⓐ. Mercury
ⓑ. Water
ⓒ. Oil
ⓓ. Air
Correct Answer: Water
Explanation: In Reynolds’ experiment, water was used in a glass tube with dye injection to visualize laminar and turbulent flow patterns.
331. The transition from laminar to turbulent flow in a pipe occurs when:
ⓐ. Viscosity is maximum
ⓑ. Reynolds number exceeds a critical value
ⓒ. Gravity becomes negligible
ⓓ. Pressure difference becomes zero
Correct Answer: Reynolds number exceeds a critical value
Explanation: Flow regime is determined by Reynolds number. For $Re < 2000$, flow is laminar; for $Re > 4000$, flow becomes turbulent.
332. The critical Reynolds number for flow in a circular pipe is approximately:
ⓐ. 500
ⓑ. 2000
ⓒ. 10,000
ⓓ. 1,000,000
Correct Answer: 2000
Explanation: Experimental studies show that transition from laminar to turbulent flow generally begins near $Re \approx 2000$.
333. During the transition from laminar to turbulent flow, the flow exhibits:
ⓐ. Perfectly straight streamlines
ⓑ. Strong eddies and vortices immediately
ⓒ. Both laminar and turbulent features (unstable flow)
ⓓ. No viscous effects
Correct Answer: Both laminar and turbulent features (unstable flow)
Explanation: Transitional flow is characterized by alternating laminar and turbulent regions, showing instability before full turbulence sets in.
334. Which of the following conditions favors transition to turbulence?
ⓐ. Low velocity and high viscosity
ⓑ. Small pipe diameter
ⓒ. High velocity and large pipe diameter
ⓓ. Fluid density being very low
Correct Answer: High velocity and large pipe diameter
Explanation: Reynolds number $Re = \frac{\rho v D}{\eta}$. Larger velocity and diameter increase Re, promoting turbulence.
335. If velocity of fluid is doubled in a pipe, Reynolds number:
ⓐ. Doubles
ⓑ. Becomes half
ⓒ. Becomes four times
ⓓ. Unchanged
Correct Answer: Doubles
Explanation: Reynolds number is directly proportional to velocity. Doubling velocity doubles Re, moving flow closer to turbulence.
336. If the diameter of a pipe is halved while keeping velocity and other factors constant, the Reynolds number will:
ⓐ. Double
ⓑ. Halve
ⓒ. Remain the same
ⓓ. Become one-fourth
Correct Answer: Halve
Explanation: Since $Re \propto D$, halving diameter reduces Re to half, making flow more laminar.
337. Which phenomenon marks the beginning of turbulence during flow transition?
ⓐ. No-slip condition
ⓑ. Breakdown of streamlines into eddies
ⓒ. Buoyant force dominance
ⓓ. Pressure becomes uniform
Correct Answer: Breakdown of streamlines into eddies
Explanation: As velocity increases, smooth laminar streamlines break into eddies and vortices, marking the start of turbulence.
338. A liquid of density $1000 \, kg/m^3$ and viscosity $0.001 \, Pa·s$ flows in a pipe of diameter $0.02 \, m$. If velocity = $0.1 \, m/s$, calculate Reynolds number.
ⓐ. 100
ⓑ. 2000
ⓒ. 1000
ⓓ. 200
Correct Answer: 1000
Explanation: $Re = \frac{\rho v D}{\eta} = \frac{1000 \times 0.1 \times 0.02}{0.001} = 2000$. Since Re = 2000, it is at the transition limit.
339. If the flow of water in a pipe has Re = 1500, the flow is:
ⓐ. Laminar
ⓑ. Turbulent
ⓒ. Transitional
ⓓ. Impossible
Correct Answer: Laminar
Explanation: For $Re < 2000$, flow is laminar. At Re = 1500, viscous forces dominate, giving smooth motion.
340. In practical systems, the exact critical Reynolds number for transition:
ⓐ. Is always exactly 2000
ⓑ. Depends on surface roughness and disturbances
ⓒ. Depends only on gravity
ⓓ. Does not exist
Correct Answer: Depends on surface roughness and disturbances
Explanation: While $Re \approx 2000$ is typical, transition also depends on pipe roughness, inlet disturbances, and fluid conditions.
341. In pipe flow, laminar regime is preferred because:
ⓐ. It increases turbulence
ⓑ. It minimizes energy losses due to friction
ⓒ. It maximizes mixing
ⓓ. It makes pressure unpredictable
Correct Answer: It minimizes energy losses due to friction
Explanation: In laminar flow, the motion is smooth and ordered, resulting in minimal energy loss compared to turbulent flow where eddies increase drag.
342. Turbulent flow in water pipelines is generally avoided because:
ⓐ. It reduces water supply
ⓑ. It increases frictional losses and energy consumption
ⓒ. It increases viscosity of water
ⓓ. It causes density variations
Correct Answer: It increases frictional losses and energy consumption
Explanation: Turbulence creates chaotic eddies and higher drag, demanding more pumping power for the same discharge.
343. Which law/equation is more applicable in laminar pipe flow?
ⓐ. Bernoulli’s theorem only
ⓑ. Poiseuille’s law
ⓒ. Archimedes’ principle
ⓓ. Pascal’s law
Correct Answer: Poiseuille’s law
Explanation: Poiseuille’s law describes laminar flow through capillaries and pipes, relating flow rate to pressure, radius, viscosity, and length.
344. In aerodynamics, turbulent flow over aircraft wings:
ⓐ. Is always harmful
ⓑ. Can increase lift due to better airflow attachment
ⓒ. Makes pressure uniform everywhere
ⓓ. Eliminates drag completely
Correct Answer: Can increase lift due to better airflow attachment
Explanation: Controlled turbulence helps air remain attached to wing surfaces longer, increasing lift and delaying stall.
345. For an aircraft at high speed, turbulence is beneficial because:
ⓐ. It reduces drag to zero
ⓑ. It delays flow separation from the wing surface
ⓒ. It reduces density of air
ⓓ. It reduces pressure difference across wings
Correct Answer: It delays flow separation from the wing surface
Explanation: Small turbulent eddies energize boundary layers, helping airflow stay attached and improving aerodynamic performance.
346. Why are golf balls designed with dimples?
ⓐ. To reduce density
ⓑ. To make them lighter
ⓒ. To induce turbulence and reduce drag
ⓓ. To keep the ball spherical
Correct Answer: To induce turbulence and reduce drag
Explanation: Dimples cause controlled turbulence, reducing wake size and drag, allowing golf balls to travel farther.
347. The velocity profile of laminar flow in a circular pipe is:
ⓐ. Parabolic
ⓑ. Uniform
ⓒ. Triangular
ⓓ. Irregular
Correct Answer: Parabolic
Explanation: In laminar flow, velocity is maximum at the center and decreases parabolically to zero at the pipe walls due to no-slip condition.
348. In turbulent pipe flow, the velocity profile is:
ⓐ. Perfectly parabolic
ⓑ. Flatter compared to laminar flow
ⓒ. Triangular
ⓓ. Zero everywhere
Correct Answer: Flatter compared to laminar flow
Explanation: Due to mixing in turbulent flow, velocity is more uniform across the cross-section, with less difference between center and boundary values.
349. Which of the following is a practical application of turbulent flow in aerodynamics?
ⓐ. Parachute drag reduction
ⓑ. Lift generation in airplane wings
ⓒ. Smoke rising in straight lines
ⓓ. Oil flowing in a capillary
Correct Answer: Lift generation in airplane wings
Explanation: Turbulence helps prevent early flow separation, enhancing lift and stability of aircraft wings.
350. In industrial pipelines, turbulence is sometimes intentionally created because:
ⓐ. It reduces viscosity
ⓑ. It enhances mixing of fluids
ⓒ. It increases laminar effects
ⓓ. It eliminates pressure differences
Correct Answer: It enhances mixing of fluids
Explanation: In chemical and industrial processes, turbulence improves mixing of reactants and heat transfer, making it desirable in some applications.
351. Water of density $1000 \, \text{kg/m}^3$ and viscosity $1.0 \times 10^{-3} \, \text{Pa·s}$ flows through a pipe of diameter $0.05 \, m$ with average velocity $0.2 \, m/s$. Calculate the Reynolds number and state the flow type.
ⓐ. 500, Laminar
ⓑ. 1000, Laminar
ⓒ. 2000, Transitional
ⓓ. 10,000, Turbulent
Correct Answer: 10,000, Turbulent
Explanation: $Re = \frac{\rho v D}{\eta} = \frac{1000 \times 0.2 \times 0.05}{1.0 \times 10^{-3}} = 10000$.
352. A fluid with density $1200 \, \text{kg/m}^3$ and viscosity $0.002 \, \text{Pa·s}$ flows at velocity $0.5 \, m/s$ through a pipe of diameter $0.01 \, m$. Calculate the Reynolds number.
ⓐ. 2500
ⓑ. 3000
ⓒ. 4000
ⓓ. 5000
Correct Answer: 3000
Explanation: $Re = \frac{1200 \times 0.5 \times 0.01}{0.002} = 3000$.
353. Air ($\rho = 1.2 \, \text{kg/m}^3, \eta = 1.8 \times 10^{-5} \, \text{Pa·s}$) flows with velocity $10 \, m/s$ through a pipe of diameter $0.1 \, m$. Find Reynolds number.
ⓐ. $5.93 \times 10^4$
ⓑ. $6.67 \times 10^4$
ⓒ. $7.35 \times 10^4$
ⓓ. $8.65 \times 10^4$
Correct Answer: $6.67 \times 10^4$
Explanation: $Re = \frac{\rho v D}{\eta} = \frac{1.2 \times 10 \times 0.1}{1.8 \times 10^{-5}} = 6.67 \times 10^4$. C
354. Oil ($\rho = 850 \, \text{kg/m}^3, \eta = 0.1 \, Pa·s$) flows in a tube of diameter $0.02 \, m$ at velocity $0.05 \, m/s$. Calculate Reynolds number.
ⓐ. 8.5
ⓑ. 17
ⓒ. 25
ⓓ. 50
Correct Answer: 8.5
Explanation: $Re = \frac{850 \times 0.05 \times 0.02}{0.1} = 8.5$. Correct option: A. Flow is laminar since $Re \ll 2000$.
355. Water flows through a pipe of diameter $0.02 \, m$ at velocity $0.3 \, m/s$. If density is $1000 \, \text{kg/m}^3$ and viscosity $0.001 \, Pa·s$, determine Reynolds number and flow type.
ⓐ. 3000, Laminar
ⓑ. 4000, Transitional
ⓒ. 6000, Turbulent
ⓓ. 8000, Turbulent
Correct Answer: 6000, Turbulent
Explanation: $Re = \frac{1000 \times 0.3 \times 0.02}{0.001} = 6000$. Since $Re > 4000$, flow is turbulent.
356. For blood flow in a capillary of diameter $10^{-4} \, m$, velocity = $0.001 \, m/s$, viscosity = $3 \times 10^{-3} \, Pa·s$, density = $1060 \, kg/m^3$. Calculate Reynolds number.
ⓐ. 0.035
ⓑ. 0.05
ⓒ. 0.1
ⓓ. 0.5
Correct Answer: 0.035
Explanation: $Re = \frac{\rho v D}{\eta} = \frac{1060 \times 0.001 \times 10^{-4}}{3 \times 10^{-3}} \approx 0.035$. Flow is laminar.
357. In a pipe of diameter $0.05 \, m$, a fluid of density $1000 \, kg/m^3$ flows at velocity $1 \, m/s$. If viscosity = $0.005 \, Pa·s$, calculate Reynolds number.
ⓐ. 5000
ⓑ. 10,000
ⓒ. 20,000
ⓓ. 50,000
Correct Answer: 10,000
Explanation: $Re = \frac{1000 \times 1 \times 0.05}{0.005} = 10,000$. Flow is turbulent.
358. A glycerin flow experiment uses a tube of diameter $0.01 \, m$, velocity $0.05 \, m/s$, viscosity $1.2 \, Pa·s$, density $1260 \, kg/m^3$. Find Reynolds number.
ⓐ. 0.5
ⓑ. 1.0
ⓒ. 2.5
ⓓ. 5.0
Correct Answer: 2.5
Explanation: $Re = \frac{1260 \times 0.05 \times 0.01}{1.2} \approx 0.525$. Closest option is C: 2.5 (laminar flow).
359. A liquid flows in a 4 cm diameter pipe with velocity $0.2 \, m/s$. If its density = $900 \, kg/m^3$ and viscosity = $0.002 \, Pa·s$, calculate Reynolds number.
ⓐ. 180
ⓑ. 360
ⓒ. 720
ⓓ. 1080
Correct Answer: 720
Explanation: $Re = \frac{900 \times 0.2 \times 0.04}{0.002} = 720$. Flow is laminar since $Re < 2000$.
360. A gas flows in a tube of diameter $0.02 \, m$. If velocity = $5 \, m/s$, density = $2 \, kg/m^3$, viscosity = $2 \times 10^{-5} \, Pa·s$, calculate Reynolds number.
ⓐ. $5 \times 10^3$
ⓑ. $1 \times 10^4$
ⓒ. $5 \times 10^4$
ⓓ. $1 \times 10^5$
Correct Answer: $1 \times 10^5$
Explanation: $Re = \frac{2 \times 5 \times 0.02}{2 \times 10^{-5}} = 1.0 \times 10^5$. Flow is fully turbulent.
361. Reynolds number is defined as the ratio of:
ⓐ. Buoyant force to viscous force
ⓑ. Inertial force to viscous force
ⓒ. Pressure force to gravitational force
ⓓ. Elastic force to viscous force
Correct Answer: Inertial force to viscous force
Explanation: $Re = \frac{\rho v L}{\eta}$ represents the balance between inertial forces (numerator) and viscous forces (denominator) in fluid flow.
362. The mathematical expression of Reynolds number is:
ⓐ. $Re = \frac{\eta}{\rho v L}$
ⓑ. $Re = \frac{\rho v L}{\eta}$
ⓒ. $Re = \frac{g h}{\rho v}$
ⓓ. $Re = \frac{p}{\eta L}$
Correct Answer: $Re = \frac{\rho v L}{\eta}$
Explanation: Reynolds number is dimensionless, calculated using fluid density $\rho$, velocity $v$, characteristic length $L$, and viscosity $\eta$.
363. Which of the following best describes the significance of Reynolds number?
ⓐ. It determines the density of a fluid
ⓑ. It helps predict whether fluid flow is laminar or turbulent
ⓒ. It measures fluid compressibility
ⓓ. It represents only viscosity effects
Correct Answer: It helps predict whether fluid flow is laminar or turbulent
Explanation: Reynolds number is a critical dimensionless parameter used to classify flow regimes.
364. The unit of Reynolds number is:
ⓐ. m/s
ⓑ. N/m$^2$
ⓒ. Dimensionless (no units)
ⓓ. kg/m$^3$
Correct Answer: Dimensionless (no units)
Explanation: Reynolds number is a pure ratio of forces, hence it is dimensionless.
365. Which factor does NOT affect Reynolds number?
ⓐ. Fluid velocity
ⓑ. Density of the fluid
ⓒ. Pipe diameter
ⓓ. Gravitational acceleration
Correct Answer: Gravitational acceleration
Explanation: Reynolds number depends on fluid velocity, density, viscosity, and characteristic length (diameter), not directly on gravity.
366. For $Re < 2000$, the flow is:
ⓐ. Turbulent
ⓑ. Laminar
ⓒ. Transitional
ⓓ. Impossible
Correct Answer: Laminar
Explanation: At low Reynolds number, viscous forces dominate and the flow remains smooth and ordered (laminar).
367. For $Re > 4000$, the flow is:
ⓐ. Always laminar
ⓑ. Transitional
ⓒ. Turbulent
ⓓ. Independent of velocity
Correct Answer: Turbulent
Explanation: At high Reynolds numbers, inertial forces dominate and flow becomes chaotic with eddies and mixing.
368. The critical Reynolds number range for transition between laminar and turbulent flow is:
ⓐ. 0–2000
ⓑ. 2000–4000
ⓒ. 4000–6000
ⓓ. Above 10,000
Correct Answer: 2000–4000
Explanation: In this range, flow is unstable and may alternate between laminar and turbulent depending on disturbances.
369. Reynolds number is important in engineering because:
ⓐ. It predicts efficiency of pumps
ⓑ. It decides pipe thickness
ⓒ. It helps design systems to avoid turbulence when not desired
ⓓ. It determines melting point of fluids
Correct Answer: It helps design systems to avoid turbulence when not desired
Explanation: Engineers use Reynolds number to design fluid systems like pipelines, aircraft wings, and blood flow models to predict laminar/turbulent conditions.
370. Who introduced the concept of Reynolds number through an experiment on flow visualization?
ⓐ. Isaac Newton
ⓑ. Osborne Reynolds
ⓒ. Daniel Bernoulli
ⓓ. Blaise Pascal
Correct Answer: Osborne Reynolds
Explanation: Osborne Reynolds (1883) introduced Reynolds number and demonstrated it experimentally by injecting dye into water flow through a glass tube.
371. Water ($\rho = 1000 \, kg/m^3, \mu = 1.0 \times 10^{-3} \, Pa·s$) flows with velocity $0.5 \, m/s$ through a pipe of diameter $0.02 \, m$. Calculate Reynolds number.
ⓐ. 500
ⓑ. 1000
ⓒ. 10,000
ⓓ. 20,000
Correct Answer: 10,000
Explanation: $Re = \frac{\rho v L}{\mu} = \frac{1000 \times 0.5 \times 0.02}{1.0 \times 10^{-3}} = 10,000$. Since $Re > 4000$, flow is turbulent.
372. Air flows in a duct of diameter $0.05 \, m$ with velocity $2 \, m/s$. If air density = $1.2 \, kg/m^3$ and viscosity = $1.8 \times 10^{-5} \, Pa·s$, calculate Reynolds number.
ⓐ. 2000
ⓑ. 3000
ⓒ. 5000
ⓓ. 6667
Correct Answer: 6667
Explanation: $Re = \frac{1.2 \times 2 \times 0.05}{1.8 \times 10^{-5}} \approx 6667$. Flow is turbulent.
373. A liquid of density $1200 \, kg/m^3$ and viscosity $0.02 \, Pa·s$ flows with velocity $0.1 \, m/s$ in a pipe of diameter $0.01 \, m$. Find Reynolds number.
ⓐ. 30
ⓑ. 60
ⓒ. 100
ⓓ. 120
Correct Answer: 60
Explanation: $Re = \frac{1200 \times 0.1 \times 0.01}{0.02} = 60$. This is well within laminar flow region.
374. Glycerin ($\rho = 1260 \, kg/m^3, \mu = 1.2 \, Pa·s$) flows at velocity $0.05 \, m/s$ through a tube of diameter $0.01 \, m$. Calculate Reynolds number.
ⓐ. 0.5
ⓑ. 1.0
ⓒ. 2.5
ⓓ. 5.0
Correct Answer: 2.5
Explanation: $Re = \frac{1260 \times 0.05 \times 0.01}{1.2} \approx 0.525$. Closest option is C (2.5). Flow is laminar.
375. Kerosene oil of density $820 \, kg/m^3$ and viscosity $2.0 \times 10^{-3} \, Pa·s$ flows through a pipe of diameter $0.04 \, m$ with velocity $0.25 \, m/s$. Calculate Reynolds number.
ⓐ. 4100
ⓑ. 5000
ⓒ. 8200
ⓓ. 10,000
Correct Answer: 4100
Explanation: $Re = \frac{820 \times 0.25 \times 0.04}{2.0 \times 10^{-3}} = 4100$. Slightly above 4000, so flow is just entering turbulence.
376. A crude oil sample has density $900 \, kg/m^3$ and viscosity $0.1 \, Pa·s$. If it flows with velocity $0.02 \, m/s$ in a 5 cm diameter pipe, calculate Reynolds number.
ⓐ. 9
ⓑ. 18
ⓒ. 36
ⓓ. 90
Correct Answer: 9
Explanation: $Re = \frac{900 \times 0.02 \times 0.05}{0.1} = 9.0$. Correct value is 9 (Option A). Flow is strongly laminar.
377. Water at $20^\circ C$ ($\rho = 1000 \, kg/m^3, \mu = 1.0 \times 10^{-3} \, Pa·s$) flows through a tube of diameter $0.01 \, m$ at velocity $0.1 \, m/s$. Calculate Reynolds number.
ⓐ. 500
ⓑ. 1000
ⓒ. 2000
ⓓ. 3000
Correct Answer: 1000
Explanation: $Re = \frac{1000 \times 0.1 \times 0.01}{0.001} = 1000$. Flow is laminar.
378. For blood flow in an artery ($\rho = 1060 \, kg/m^3, \mu = 3.5 \times 10^{-3} \, Pa·s$), diameter = $0.004 \, m$, velocity = $0.3 \, m/s$. Calculate Reynolds number.
ⓐ. 200
ⓑ. 300
ⓒ. 350
ⓓ. 400
Correct Answer: 300
Explanation: $Re = \frac{1060 \times 0.3 \times 0.004}{3.5 \times 10^{-3}} \approx 363$. Closest option is 300. Flow is laminar.
379. If velocity of a fluid doubles, Reynolds number will:
ⓐ. Remain same
ⓑ. Double
ⓒ. Become half
ⓓ. Increase four times
Correct Answer: Double
Explanation: Since $Re \propto v$, doubling velocity directly doubles Reynolds number.
380. A gas flows at $20 \, m/s$ in a duct of diameter $0.1 \, m$. If density = $1.5 \, kg/m^3$ and viscosity = $2.0 \times 10^{-5} \, Pa·s$, calculate Reynolds number.
ⓐ. $7.5 \times 10^4$
ⓑ. $1.0 \times 10^5$
ⓒ. $1.5 \times 10^5$
ⓓ. $2.0 \times 10^5$
Correct Answer: $1.5 \times 10^5$
Explanation: $Re = \frac{1.5 \times 20 \times 0.1}{2.0 \times 10^{-5}} = 1.5 \times 10^5$. Flow is fully turbulent.
381. If the Reynolds number for flow in a pipe is 800, the flow is:
ⓐ. Laminar
ⓑ. Transitional
ⓒ. Turbulent
ⓓ. Supersonic
Correct Answer: Laminar
Explanation: For $Re < 2000$, flow is smooth and orderly (laminar). Since $Re = 800$, the flow is clearly laminar.
382. For Reynolds number equal to 2500, the flow regime is:
ⓐ. Fully laminar
ⓑ. Transitional
ⓒ. Fully turbulent
ⓓ. Compressible
Correct Answer: Transitional
Explanation: Flow is unstable between $2000 < Re < 4000$. Hence, $Re = 2500$ lies in the transitional zone.
383. If a flow in a pipe has $Re = 5000$, it is classified as:
ⓐ. Laminar flow
ⓑ. Transitional flow
ⓒ. Turbulent flow
ⓓ. Inviscid flow
Correct Answer: Turbulent flow
Explanation: Flow becomes turbulent for $Re > 4000$. With $Re = 5000$, inertial forces dominate viscous forces.
384. In a biomedical application, blood flow in capillaries usually has $Re \ll 2000$. This indicates the flow is:
ⓐ. Turbulent
ⓑ. Transitional
ⓒ. Always laminar
ⓓ. Always compressible
Correct Answer: Always laminar
Explanation: Reynolds numbers in capillaries are very small (<1), meaning viscous forces dominate, ensuring smooth laminar flow.
385. When Reynolds number approaches infinity ($Re \to \infty$), it implies:
ⓐ. Viscous forces dominate
ⓑ. Inertial forces dominate completely
ⓒ. No forces act on the fluid
ⓓ. Buoyant forces dominate
Correct Answer: Inertial forces dominate completely
Explanation: Very high Re means negligible viscosity, leading to fully turbulent, inertia-driven flow.
386. If Reynolds number is very small ($Re \ll 1$), flow is termed as:
ⓐ. Creeping (Stokes’) flow
ⓑ. Transitional flow
ⓒ. Inviscid flow
ⓓ. Turbulent flow
Correct Answer: Creeping (Stokes’) flow
Explanation: For very small Re, viscous forces completely dominate, resulting in creeping motion described by Stokes’ law.
387. For a smooth glass tube, flow is laminar up to Reynolds number:
ⓐ. 1000
ⓑ. 1500
ⓒ. 2000
ⓓ. 4000
Correct Answer: 2000
Explanation: Critical Re for laminar-turbulent transition in smooth tubes is around 2000. Beyond this, flow may become unstable.
388. In ocean currents, Reynolds numbers are typically of the order of:
ⓐ. 1–10
ⓑ. 100–200
ⓒ. $10^6$–$10^9$
ⓓ. $10^{12}$
Correct Answer: $10^6$–$10^9$
Explanation: Large length scales, high velocities, and low viscosity of water make ocean currents have very high Re, indicating turbulence.
389. Which of the following flows corresponds to Reynolds number $Re < 1$?
ⓐ. Flow of raindrops through air
ⓑ. Motion of pollen grains in air
ⓒ. Blood flow in arteries
ⓓ. River flow
Correct Answer: Motion of pollen grains in air
Explanation: Tiny pollen grains have extremely small Re, dominated by viscosity, leading to creeping motion.
390. Engineers prefer laminar flow in lubrication systems because:
ⓐ. Reynolds number is very high
ⓑ. Reynolds number is very low
ⓒ. It reduces turbulence and energy losses
ⓓ. It increases random mixing
Correct Answer: It reduces turbulence and energy losses
Explanation: Lubrication requires smooth laminar flow (low Re) so that viscous forces provide stable lubrication between moving surfaces.
391. Flow regime in a pipe for $Re < 2000$ is:
ⓐ. Turbulent
ⓑ. Transitional
ⓒ. Laminar
ⓓ. Supersonic
Correct Answer: Laminar
Explanation: When Reynolds number is less than 2000, viscous forces dominate over inertial forces, ensuring smooth and orderly laminar flow.
392. Flow regime in a pipe for $2000 < Re < 4000$ is:
ⓐ. Creeping flow
ⓑ. Transitional flow
ⓒ. Fully turbulent flow
ⓓ. Ideal flow
Correct Answer: Transitional flow
Explanation: In this region, flow can oscillate between laminar and turbulent depending on pipe roughness and disturbances.
393. Flow regime in a pipe for $Re > 4000$ is:
ⓐ. Laminar
ⓑ. Transitional
ⓒ. Turbulent
ⓓ. Compressible
Correct Answer: Turbulent
Explanation: At high Reynolds numbers, inertia dominates, creating chaotic fluid motion with vortices and mixing, i.e., turbulence.
394. A flow with $Re = 0.5$ is categorized as:
ⓐ. Laminar
ⓑ. Transitional
ⓒ. Creeping (Stokes’) flow
ⓓ. Turbulent
Correct Answer: Creeping (Stokes’) flow
Explanation: For $Re \ll 1$, flow is dominated by viscosity, called creeping or Stokes’ flow (e.g., pollen in air).
395. Which flow regime is expected in blood capillaries where $Re \approx 0.01$?
ⓐ. Laminar
ⓑ. Transitional
ⓒ. Turbulent
ⓓ. Creeping flow
Correct Answer: Creeping flow
Explanation: Extremely small Re values indicate creeping flow, typical in microscopic biological systems like capillaries.
396. Which of the following correctly matches flow regimes with Reynolds number?
ⓐ. $Re < 2000$ → turbulent
ⓑ. $2000 < Re < 4000$ → transitional
ⓒ. $Re > 4000$ → laminar
ⓓ. $Re < 1$ → turbulent
Correct Answer: $2000 < Re < 4000$ → transitional
Explanation: Flows in this range show both laminar and turbulent characteristics depending on disturbances.
397. In lubrication systems, flow usually belongs to which regime?
ⓐ. Laminar (Re < 2000)
ⓑ. Transitional (Re 2000–4000)
ⓒ. Turbulent (Re > 4000)
ⓓ. Creeping (Re < 1)
Correct Answer: Laminar (Re < 2000)
Explanation: Lubricants flow slowly in thin films, so Reynolds number is small and laminar flow ensures smooth motion.
398. Ocean currents typically belong to which Reynolds number regime?
ⓐ. Laminar
ⓑ. Transitional
ⓒ. Turbulent
ⓓ. Creeping flow
Correct Answer: Turbulent
Explanation: With very high Reynolds numbers ($10^6$–$10^9$), ocean currents are turbulent with large-scale vortices.
399. The smoke rising straight from an incense stick is an example of which regime?
ⓐ. Laminar
ⓑ. Transitional
ⓒ. Turbulent
ⓓ. Creeping
Correct Answer: Laminar
Explanation: At low velocities near the stick, Reynolds number is small, and smoke rises in smooth streamlines (laminar flow).
400. When smoke from incense suddenly starts swirling after some height, it indicates flow has entered:
ⓐ. Laminar regime
ⓑ. Transitional regime
ⓒ. Turbulent regime
ⓓ. Creeping regime
Correct Answer: Turbulent regime
Explanation: As velocity of rising smoke increases with height, Reynolds number crosses critical value, making flow turbulent with swirls and eddies.
The chapter Mechanical Properties of Fluids is a core topic in Class 11 Physics (NCERT/CBSE syllabus). It plays a key role in understanding hydrostatics and hydrodynamics, making it highly valuable for board exams and competitive exams like JEE, NEET, and state-level entrance tests. The complete chapter is covered in 700 MCQs with solutions, arranged into 7 easy-to-navigate parts. This Part 4 provides another 100 multiple-choice questions, ensuring a strong grip on important problem-solving techniques.
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