Bernoulli's Theorem & Continuity — Practice Questions

Free NEET Physics multiple-choice questions on Bernoulli's Theorem & Continuity. Attempt each question and reveal the answer with a full explanation.

A venturimeter is used to measure: Rate of flow of liquid Liquid density Liquid pressure Liquid viscosity For a fluid flow through a pipe to be turbulent, the Reynolds number ( R e ) should generally be: > 2000 < 1000 Between 1000 and 2000 Exactly 0 An ideal fluid flows through a horizontal pipe of varying cross-section. If the ratio of the radii at two points is 1:2 , the ratio of the velocities of flow at these points is: 4:1 2:1 1:4 1:2 For a flow of liquid in a pipe to remain laminar, the Reynolds number should be less than approximately: 2000 1000 3000 500 If the Reynolds number is less than 1000 , the flow of liquid is: Laminar Turbulent Unsteady Viscous A liquid is flowing through a horizontal pipe of varying cross-section. The ratio of the areas of cross-section at two points is 4:1 . The ratio of the velocities of the liquid at these points is: 1 : 4 4 : 1 2 : 1 1 : 2 The surface tension of which of the following liquid is maximum :- C6H6 H2O C2H5OH CH3OH The wettability of a surface by a liquid depends primarily on Viscosity Surface tension Density Angle of contact between the surface and the liquid A capillary tube of radius r is immersed in water and water rises in it to a height h . The mass of the water in the capillary is 5 g . Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is : 5.0 g 10.0 g 20.0 g 2.5 g If a soap bubble expands, the pressure inside the bubble Increases Remains the same Is equal to the atmospheric pressure Decreases A thin flat circular disc of radius 4.5 cm is placed gently over the surface of water. If surface tension of water is 0.07 N m -1 , then the excess force required to take it away from the surface is 19.8 mN 198 N 1.98 mN 99 N Which of the following is an example of an application of Bernoulli's principle? Dynamic lift of an airplane wing Capillary rise Hydraulic brake system Thermal expansion of a metal rod A fluid is in streamline flow across a horizontal pipe of variable area of cross section. For this which of the following statements is correct? Velocity is maximum at the narrowest part of the pipe and pressure is minimum there. Velocity is minimum at the narrowest part of the pipe and pressure is maximum there. Velocity is maximum at the narrowest part of the pipe and pressure is maximum there. Both velocity and pressure are maximum at the narrowest part of the pipe. A small hole of area of cross-section 2 mm 2 is present near the bottom of a fully filled open tank of height 2 m . Taking g = 10 m/s 2 , the rate of flow of water through the open hole would be nearly: 12.6 10 -6 m 3 /s 8.9 10 -6 m 3 /s 2.23 10 -6 m 3 /s 6.4 10 -6 m 3 /s The speed of efflux of a liquid from a small hole in a tank filled to a height h is v . If the tank is closed and an additional pressure P is applied to the top surface, the new speed of efflux is ( d is the density of liquid): 2gh + 2P d 2gh + P d 2gh 2P d The rate of flow of a liquid through a capillary tube of radius r is V . If the radius of the tube is doubled and length is halved, the rate of flow under the same pressure difference will be: 32V 16V 8V 4V The speed of a swimmer in still water is 20 m/s . The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is given by: 30 ∘ West 30 ∘ East 60 ∘ West 45 ∘ West A water tank has a small hole in its side at a height y from the bottom. If the water level in the tank is H , the range of the water jet on the ground is: 2√ y(H-y) √ 2y(H-y) 2√ yH √ yH Blood flow through an artery is constricted by a plaque. At the constriction, compared to the wider part: Velocity is higher, pressure is lower Velocity is higher, pressure is higher Velocity is lower, pressure is higher Velocity is lower, pressure is lower A cylindrical tank has a small hole near the bottom. The velocity of efflux does NOT depend on: The area of the hole The height of the liquid level The acceleration due to gravity The density of the liquid A tank is filled with water to a height H . A small hole is made at the bottom. The time taken for the water level to fall from H to H/2 is t 1 and from H/2 to zero is t 2 . The ratio t 1/t 2 is: 2 - 1 2 + 1 2 1/ 2 An aircraft wing is designed so that the velocity of air above the wing is 100 m/s and below the wing is 80 m/s . If the density of air is 1.3 kg/m 3 and the wing area is 20 m 2 , the dynamic lift on the wing is: 46800 N 23400 N 93600 N 11700 N In a horizontal pipe flow, if the velocity of an ideal fluid increases from v to 2v at a constriction, the pressure P changes to P' . The difference (P - P') is: 3 2 v 2 v 2 1 2 v 2 2 v 2 The pressure of water in a pipe when the tap is closed is 3 10 5 N/m 2 . When the tap is opened, the pressure reduces to 2.5 10 5 N/m 2 . The velocity of water flowing out is: 10 m/s 5 m/s 1 m/s 20 m/s The speed of air above the wings of an airplane is 120 m/s and below the wings it is 90 m/s . If the density of air is 1.3 kg/m 3 , the pressure difference between the two surfaces of the wing is: 4095 Pa 3150 Pa 2047.5 Pa 5200 Pa An ideal fluid flows through a horizontal pipe of varying cross-section. If the velocity of flow at a point where the pressure is P is v , then the pressure at a point where the velocity is 2v is (density of fluid is ): P - 3 2 v 2 P - v 2 P + 3 2 v 2 P - 2 v 2 A Pitot tube is used to measure the flow speed of a fluid of density . If the difference in the heights of the liquid levels in the manometer is h and the manometer liquid density is m , the flow speed is: 2gh m / 2gh / m gh m / 2gh m / A liquid is flowing through a horizontal pipe. At two points, the radii are r 1 and r 2 . If the pressure difference between these points is P , the rate of flow Q (volume per unit time) is proportional to: P P ( P) 2 1/ P A certain number of spherical drops of a liquid of radius 'r' coalesce to form a single drop of radius 'R' and volume 'V'. If 'T' is the surface tension of the liquid, then : energy = 4VT ( 1 r - 1 R ) is released energy = 3VT ( 1 r + 1 R ) is absorbed energy = 3VT ( 1 r - 1 R ) is released Energy is neither released nor absorbed A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5 10 -2 N/m. The pressure inside the bubble equals at a point z 0 below the free surface of water in a container. Taking g = 10 m/s 2 , density of water = 10 3 kg/m 3 , the value of z 0 is : 0.5 cm 100 cm 10 cm 1 cm The amount of energy required to form a soap bubble of radius 2 cm from a soap solution is nearly (surface tension of soap solution = 0.03 N m -1 ) 30.16 10 -4 J 5.06 10 -4 J 3.01 10 -4 J 50.1 10 -4 J A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is 250 m 2 . Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be ( P air = 1.2 kg/m 3 ): 2.4 10 5 N , upwards 2.4 10 5 N , downwards 4.8 10 5 N , upwards 4.8 10 5 N , downwards A large cylindrical tank has a hole of area A at its bottom. Water is poured into the tank by a tube of cross-sectional area a at a constant rate Q ( m 3/s ). The maximum height to which water can rise in the tank is: Q 2 / (2gA 2) Q / (2gA) Q 2 / (gA 2) 2Q 2 / (gA 2) The maximum velocity of a fluid in a pipe for which the flow remains streamline is called: Critical velocity Terminal velocity Escape velocity Efflux velocity In a horizontal pipe, at a location where the area of cross-section is 10 cm 2 , the velocity is 1 m/s and pressure is 2000 Pa . What is the pressure at a location where the area is 5 cm 2 ? (Density of liquid = 1000 kg/m 3 ) 500 Pa 1000 Pa 1500 Pa 0 Pa A venturimeter is connected to a horizontal pipe. If the area of cross-section at the entrance and the throat are A and a , and the pressure difference is h of liquid (density ρ ), then the rate of flow is: Aa √ 2gh A 2 - a 2 Aa √ 2gh A 2 + a 2 A √ 2ghA 2 a 2 a √ 2gh A 2 A liquid of density is coming out of a hose pipe of radius a with horizontal speed v and hits a mesh. 50 % of the liquid passes through the mesh unaffected. 25 % of the liquid loses all of its momentum and 25 % of the liquid recoils with the same speed. The resultant pressure on the mesh will be: 3 4 v 2 1 4 v 2 1 2 v 2 v 2 A liquid is flowing through a horizontal pipe. At a point where the radius is r , the velocity is v and pressure is P . At another point where the radius is r/2 , the pressure is P/4 . The density of the liquid is: P 10v 2 P 2v 2 P 5v 2 P v 2 Consider a water tank shown in the figure. It has one wall at x=L and can be taken to be very wide in the z direction. When filled with a liquid of surface tension S and density , the liquid surface makes angle 0 ( 0 1 ) with the x-axis at x=L . If y(x) is the height of the surface then the equation for y(x) is: (take (x)= (x)= (x)= dy dx ; g is the acceleration due to gravity) dy dx = g S x d 2y dx 2 = g S x d 2y dx 2 = g S y d 2y dx 2 = g S Water flows in a streamline motion through a horizontal pipe of circular cross-section as shown in the figure. The pressure difference of water between P and Q is 15 N m -2 . The area of cross-section at P and Q are 40 cm 2 and 20 cm 2 respectively. The rate of flow of water through the pipe, in cm 3 s -1 , is: [Take density of water =1000 kg m -3 ] 100 200 300 400 Water is flowing through a horizontal pipe of non-uniform cross-section. At a point where the radius of the pipe is 2 cm , the velocity of flow is 2 m/s . The velocity of flow at a point where the radius is 1 cm is: 8 m/s 4 m/s 1 m/s 16 m/s A liquid is flowing in a horizontal pipe. At a certain point, the velocity of the liquid increases. Which of the following is correct according to Bernoulli's principle? The pressure at that point decreases The pressure at that point increases The pressure remains constant The potential energy increases The cylindrical tube of a spray pump has radius R , one end of which has n fine holes, each of radius r . If the speed of the liquid in the tube is v , the speed of the ejection of the liquid through the holes is: v R 2 n r 2 v R 2 n 2 r 2 v R n r v 2 R n r An ideal fluid flows through a pipe of circular cross-section made of two sections with radii 2r and r . If the velocity in the first section is v , the velocity in the second section is: 4v 2v v/2 v/4 An atomizer (spray pump) works on the principle of: Bernoulli's Theorem Pascal's Law Archimedes' Principle Newton's Law of Viscosity