Fluid Mechanics Physics - Fluid Mechanics

Water is flowing through a long horizontal tube. Let P_A and P_B be the pressures at two points A and B of the tube.

1. P_A must be equal to P_B.
2. P_A must be greater than P_B.
3. P_A must be smaller than P_B.
4. P_A = P_B only if the cross- sectional area at A and B are equal.

Bernoulli's theorem is based on conservation of:

1. Momentum.
2. Mass.
3. Energy.
4. Angular momentum.

Equal mass of three liquids are kept in three identical cylindrical vessels A, B and C. The densities are P_A, P_B, P_C with P_A < P_B < P_C  The force on the base will be:

1. Maximum in vessel A.
2. Maximum in vessel B.
3. Maximum in vessel C.
4. Equal in all the vessels.

Why is it easier to swim in sea water than in fresh water?

A cubical box is to be constructed with iron sheets 1mm in thickness. What can be the minimum value of the external edge so that the cube does not sink in water? Density of iron = 8000kg/m³ and density of water = 1000kg/m³.

Water is slowly coming out from a vertical pipe. As the water descends after coming out, its area of cross-section reduces. Explain this on the basis of the equation of continuity.

The free surface of a liquid resting in an inertial frame is horizontal. Does the normal to the free surface pass through the centre of the earth? Think separately if the? The free surface of a liquid resting in an inertial frame is horizontal. Does the normal to the free surface pass through the centre of the earth? Think separately if the liquid is.

1. At the equator.
2. At a pole.
3. Somewhere else.

A glass of water has an ice cube floating in water. The water level just touches the rim of the glass. will the water overflow when the ice melts? 

A U- tube containing a liquid is accelerated horizontally with a constant acceleration a₀. If the separation between the vertical limbs is 1, find the difference in the heights of the liquid in the two arms.

Water flows through a horizontal tube of variable cross-section. The area of cross-section at A and B are 4mm² and 2mm² respectively. If 1cc of water enters per second through A, find,

1. The speed ofwater at A.
2. The speed of water at B.
3. Thepressure difference P_A - P_B.

A wooden block of mass 0.5kg and density 800kg/m³ is fastened to the free end of a vertical spring of spring constant 50N/m fixed at the bottom. If the entire system is completely immersed in water, find.

1. The elongation (or compression) of the spring in equilibrium and.
2. The time-period of vertical oscillations of the block when it is slightly depressed and released.

The heights of mercury surfaces in the two arms of the manometer shown in figure are 2cm and 8cm. Atmospheric pressure = 1. 01 x 10⁵N/rn². Find.

1. Thepressure of the gas in the cylinder and.
2. The pressure of mercury at the bottom of the U tube.

A cube of ice of edge 4cm is placed in an empty cylindrical glass of inner diameter 6cm. Assume that the ice melts uniformly from each side so that it always retains its cubical shape. Remembering that ice is lighter than water, find the length of the edge of the ice cube at the instant it just leaves contact with the bottom of the glass.

A cylindrical object of outer diameter 10cm, height 20cm and density 8000kg/m³ is supported by a vertical spring and is half dipped in water as shown in.

1. Find the elongation of the spring in equilibrium condition.
2. If the object is slightly depressed and released, find the time period of resulting oscillations of the object. The spring constant = 500N/m.

A glass full of water has a bottom of area 20cm², top of area 20cm², height 20cm and volume half a litre.

1. Find the force exerted by the water on the bottom.
2. Considering the equilibrium of the water, find the.

Resultant force exerted by the sides of the glass on the water. Atmospheric pressure = 1.0 × 10⁵N/m². Density of water = 1000kg/m³ and g = 10m/s². Take all numbers to be exact.

Water is filled in a rectangular tank of size 3m × 2m × 1m.

1. Find the total force exerted by the water on the bottom surface of the tank.
2. Consider a vertical side of area 2m × 1m. Take a horizontal strip of width ox metre in this side, situated at a depth of x metre from the surface of water. Find the force by the water on this strip.
3. Find the torque of the force calculated in part.(b) about the bottom edge of this side.
4. Find the total force by the water on this side.
5. Find the total torque by the water on the side about.

The bottom edge. Neglect the atmospheric pressure and take g = 10m/s².

Suppose the glass of the previous problem is covered by a jar and the air inside the jar is completely pumped out.

1. What will be the answers to the problem?
2. Show that the answers do not change if a glass of different shape is used provided the height, the bottom area and the volume are unchanged.

Suppose the density of air at Madras is P₀ and atomospheric pressure is P₀. If we go up, the density and the pressure both decrease. Suppose we wish to calculate the pressure at a height 10km above Madras. If we use the equation P₀ - P = pogz, will we get a pressure more than the actual or less than the actual? Neglect the variation in g. Does your answer change if you also consider the variation in g?

In the derivation of P₁ - P₂ = Pgz, it was assumed that the liquid is incompressible. Why will this equation not be strictly valid for a compressible liquid?

While watering a distant plant, a gardener partially water than in fresh closes the exit hole of the pipe by putting his finger on it. Explain why this results in the water stream goirig to a larger distance.

Refer to the previous problem. Suppose, the goldsmith argues that he has not mixed copper or any other material with gold, rather some cavities might have been left inside the ornament. Calculate the volume of the cavities left that will allow the weights given in that problem.

A cubical metal block of edge 12cm floats in mercury with one fifth of the height inside the mercury. Water is poured till the surface of the block is just immersed in it. Find the height of the water column to be poured. Specific gravity of mercury = 13.6.

Water leaks out from an open tank through a hole of area 2mm² in the bottom. Suppose water is filled up to a height of 80cm and the area of cross-section of the tank is 0.4m². The pressure at the open surface and at the hole are equal to the atmospheric pressure. Neglect the small velocity of the water near the open surface in the tank.

1. Find the initial speed of water coming out of the hole.
2. Find the speed of water coming out when half of water has leaked out.
3. Find the volume of water leaked out during a time interval dt after the height remained is h. Thus find the decrease in height dh in terms of h and dt.
4. From the result of part c find the time required for half of the water to leak out.

An ornament weighing 36g in air, weighs only 34g in water. Assuming that some copper is mixed with gold to prepare the ornament, find the amount of copper in it. Specific gravity of gold is 19.3 and that of copper is 8.9.