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