Mechanical Properties of Fluids

A submarine is designed to withstand an absolute pressure of 100 atm. How deep can it go below the water surface ? (Consider the density of water = 1000 kg m-3, 1 atm = 1 105 Pa and gravitational acceleration g = 10 m/s2)

1. 9900 m
2. 990 m
3. 9000 m
4. 99 m

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 cm2 and 20 cm2, respectively. The rate of flow of water through the pipe, in cm3 s-1, is: [Take density of water = 1000 kg m-3] [figure]

1. 400
2. 100
3. 200
4. 300

In the measurement of viscosity of liquids using terminal velocity experiment, spherical balls of same radius but having different densities are used. The variation of the terminal velocity (v) with the ratio of density of spherical ball ( ) to density of the liquid ( ), is best represented by:

1. [figure]
2. [figure]
3. [figure]
4. [figure]

A balloon is made of a material of surface tension S and its inflation outlet (from where gas is filled in it) has small area A. It is filled with a gas of density and takes a spherical shape of radius R. When the gas is allowed to flow freely out of it, its radius r changes from R to 0 (zero) in time T. If the speed v(r) of gas coming out of the balloon depends on r as ra and T S A R then

1. a = - 12, = - 12, = -1, = 12, = 72
2. a = 12, = 12, = - 12, = 12, = 72
3. a = 12, = 12, = -1, = +1, = 32
4. a = - 12, = - 12, = -1, = - 12, = 52

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: [figure] (take (x) = (x) = (x) = dydx, g is the acceleration due to gravity)

1. d2ydx2 = gS
2. dydx = gSx
3. d2ydx2 = gSx
4. d2ydx2 = gSy

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

1. 19.8 mN
2. 198 N
3. 1.98 mN
4. 99 N

An ideal fluid is flowing in a non-uniform cross-sectional tube XY (as shown in the figure) from end X to end Y. If K1 and K2 are the kinetic energy per unit volume of the fluid at X and Y respectively, then the correct option is : [figure]

1. K1 = K2
2. 2K1 = K2
3. K1 > K2
4. K1 < K2

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)

1. 5.06 10-4 J
2. 3.01 10-4 J
3. 50.1 10-4 J
4. 30.16 10-4 J

The venturi-meter works on :

1. Bernoulli's principle
2. The principle of parallel axes
3. The principle of perpendicular axes
4. Huygens' principle

A spherical ball is dropped in a long column of a highly viscous liquid. The curve in the graph shown, which represents the speed of the ball (v) as a function of time (t) is [figure]

1. A
2. B
3. C
4. D

If a soap bubble expands, the pressure inside the bubble

1. Decreases
2. Increases
3. Remains the same
4. Is equal to the atmospheric pressure

Two copper vessels A and B have the same base area but of different shapes. A takes twice the volume of water as that B requires to fill upto a particular common height. Then the correct statement among the following is :

1. Vessel B weighs twice that of A.
2. Pressure on the base area of vessels A and B is same.
3. Pressure on the base area of vessels A and B is not same.
4. Both vessels A and B weigh the same.

The terminal velocity of a copper ball of radius 5 mm falling through a tank of oil at room temperature is 10 cm s-1. If the viscosity of oil at room temperature is 0.9 kg m-1 s-1, the viscous drag force is :

1. 4.23 10-6 N
2. 8.48 10-3 N
3. 8.48 10-5 N
4. 4.23 10-3 N

The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerin becomes constant after some time. If the density of glycerin is d2, then the viscous force acting on the ball will be :

1. 2Mg
2. Mg2
3. Mg
4. 32Mg

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 :

1. 5.0 g
2. 10.0 g
3. 20.0 g
4. 2.5 g

A small hole of area of cross-section 2 mm2 is present near the bottom of a fully filled open tank of height 2 m. Taking g = 10 m/s2, the rate of flow of water through the open hole would be nearly :

1. 8.9 10-6 m3/s
2. 2.23 10-6 m3/s
3. 6.4 10-6 m3/s
4. 12.6 10-6 m3/s

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 the pressure at a point Z0 below the free surface of water in a container. Taking g = 10 m/s2, density of water = 103 kg/m3, the value of Z0 is :

1. 1 cm
2. 10 cm
3. 100 cm
4. 0.5 cm

A small sphere of radius 'r' falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to

1. r3
2. r2
3. r5
4. r4

A U tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is [figure]

1. 425 kg m-3
2. 800 kg m-3
3. 928 kg m-3
4. 650 kg m-3

Two non-mixing liquids of densities and n (n > 1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length pL (p < 1) in the denser liquid. The density d is equal to

1. \2 + (n - 1)p\
2. \1 + (n - 1)p\
3. \1 + (n + 1)p\
4. \2 + (n + 1)p\

A rectangular film of liquid is extended from (4 cm 2 cm) to (5 cm 4 cm). If the work done is 3 10-4 J, the value of the surface tension of the liquid is

1. 0.250 N m-1
2. 0.125 N m-1
3. 0.2 N m-1
4. 8.0 N m-1

Three liquids of densities 1, 2 and 3 (with 1 > 2 > 3), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact 1, 2 and 3 obey

1. 2 > 1 > 2 > 3 0
2. 0 1 < 2 < 3 < 2
3. 2 < 1 < 2 < 3 <
4. > 1 > 2 > 3 > 2

The heart of a man pumps 5 litres of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be 13.6 103 kg/m3 and g = 10 m/s2 then the power (in watt) is

1. 3.0
2. 1.50
3. 1.70
4. 2.35

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

1. VR2n3r2
2. V2Rnr
3. VR2n2r2
4. VR2nr2

Water rises to a height h in capillary tube. If the length of capillary tube above the surface of water is made less than h, then

1. water rises upto a point a little below the top and stays there.
2. water does not rise at all.
3. water rises upto the tip of capillary tube and then starts overflowing like a fountain.
4. water rises upto the top of capillary tube and stays there without overflowing.

A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is 250 m2. 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 ( air = 1.2 kg/m3)

1. 2.4 105 N, upwards
2. 2.4 105 N, downwards
3. 4.8 105 N, downwards
4. 4.8 105 N, upwards

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

1. energy = 4VT ( 1r - 1R ) is released.
2. energy = 3VT ( 1r + 1R ) is absorbed.
3. energy = 3VT ( 1r - 1R ) is released.
4. energy is neither released nor absorbed.

The wettability of a surface by a liquid depends primarily on

1. density
2. angle of contact between the surface and the liquid
3. viscosity
4. surface tension

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?

1. The velocity is maximum at the narrowest part of the pipe and pressure is maximum at the widest part of the pipe.
2. Velocity and pressure both are maximum at the narrowest part of the pipe.
3. Velocity and pressure both are maximum at the widest part of the pipe.
4. The velocity is minimum at the narrowest part of the pipe and the pressure is minimum at the widest part of the pipe.