Concepts of Physics Ch-13 Fluid Mechanics (SA)

1. Is it always true that the molecules of a dense liquid are heavier than the molecules of a lighter liquid ?

Solution: Density is defined as mass per unit volume. It tells how closely packed are the molecules inside an object. When molecules are tightly packed, we say that the object is dense; when molecules are far apart, we say that the object is light.

The density of a liquid depends on the mass of the molecules that make up the liquid and the closeness of the molecules of the liquid. It is not always true that the molecules of a dense liquid are heavier than the molecules of a lighter liquid.

For example, alcohol is less dense than oil. Alcohol molecules are mostly carbon and hydrogen atoms, so they are similar to oil. But they also contain an oxygen atom, which makes them a little heavy. For this reason, you might think that alcohol is denser than oil. But because of their shape and size, alcohol molecules do not pack as efficiently as oil molecules. This property of molecules makes alcohol less dense than oil.

2. If someone presses a pointed needle against your skin, you are hurt. But if someone presses a rod against your skin with the same force, you easily tolerate. Explain.

Solution: We know that pressure is the application of force over a particular area. In mathematical terms, pressure is equal to force divided by area; that is, with more force comes more pressure and with more area comes less pressure. An iron rod has more surface area than the pointed tip of the needle. That is why the pointed needle exerts more pressure than the iron rod (with the same force) when pressed against our skin.

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

Solution: In case of an incompressible liquid, the density is independent of the variations in pressure and always remains constant. But it is not so in case of a compressible liquid. Thus, the given equation will not be strictly valid for a compressible liquid.

4. Suppose the density of air at Madras is and atmospheric pressure is P0. If we go up, the density and the pressure both decrease. Suppose we wish to calculate the pressure at a height 10 km above Madras. If we use the equation P0-P= ρ0gz, 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?

Solution: Using the equation, P0-P= ρ0gz , we get P=P0- ρ0gz

                        The pressure calculated by using this equation will be more than the actual pressure because density at a height of 10 km above Madras will be less than ρ0.

            Yes, the answer will change if we also consider the variation in g. Because g decreases with height, it will have the same effect on pressure as that of density.

5. 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 (a) at the equator (b) at a pole (c) somewhere else.

Solution: Yes, the normal to the free surface of the liquid passes through the centre of the earth. Because of the gravitational force, the free surface o the liquid takes the shape of the surface of the Earth. Also, because the gravitational force is directed towards the centre of the earth, the normal to the free surface also passes through the centre of the Earth (in all cases).

6. A barometer tube reads 76 cm of mercury. If the tube is gradually inclined keeping the open end immersed in the mercury reservoir, will the length of mercury column be 76 cm, more than 76 cm or less than 76 cm ?

Solution: The length of the mercury column will be more than 76 cm.

7. A one meter long glass tube is open at both ends. One end of the tube is dipped into a mercury cup, the tube is kept vertical and the air is pumped out of the tube by connecting the upper end to a suction pump.’ Can mercury be pulled up into the pump by this process?

Solution:  No, mercury cannot be pulled up into the pump by this process. The level up to which mercury can rise is 76 cm (to maintain equal pressure at points A and B)

8. A satellite revolves round the earth. Air pressure inside the satellite is maintained at 76 cm of mercury. What will be the height of mercury column in a barometer tube 1 m long placed in the satellite ?

Solution: Pressure at point A is 76 cm of mercury. Therefore, mercury will rise to full length of the tube, i.e., 1 m, to maintain equal pressure at points A and B inside the satellites.

                Geffective=0, so the pressure due to height of the mercury column will be zero.

9. Consider the barometer shown in the figure (13-Q1). If a small hole is made at a point P in the barometer tube will the mercury come out from this hole?

Solution: Two pressures are acting upon point P:

            (i) Pressure due to mercury level above point  P equals to P1 (say)

            (ii) Atmospheric pressure =  P0 (inwards) And, P0>P1

As the inward pressure is more, the mercury will not come out of the hole.

10. Is Archimedes’ principle valid in an elevator accelerating up? In a car accelerating on a level road?

Solution: Archimedes principle is not valid in case of an elevator accelerating upwards, but it is valid for a car accelerating on a level road.

According to Archimedes’ principle, Buoyant force, B= Weight of the substituted liquid or, B = mg.

The above principle is satisfied in case of a car accelerating on a level road. In case of an elevator, the buoyant force will be as below: B = mg + ma (if the elevator is going upwards with acceleration ‘a’)

Thus, Archimedes’ principle is not valid in this case.

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

Solution: Whether an object sinks or floats in a liquid depends upon the density of the two. We know that sea water has dissolved salts in it, which increase its density. So, sea water exerts more buoyancy  force (in the upward direction) on the swimmer than that exerted by fresh water. This helps the person to swim easily in sea water compared to fresh water.

12. 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?

Solution: The water of mass is equal to the mass of the ice cube will take less volume compared to the ice cube. The water will not overflow when the ice melts because the ice will displace the space I would take if it were in a liquid state.

13. A ferry boat loaded with rocks has to pass under a bridge. The maximum height of the rocks is slightly more than the height of the bridge so that the boat just fails to pass under the bridge. Should some of the rocks be removed or some more rocks be added?

Solution: Some rocks should be added to increase the force acting in the downward direction. It will help the boat to pass under the bridge. If some rocks are removed, the up thrust of water on the boat will be greater than the weight of the boat. So, the boat will rise in water and will fail to pass under the bridge.

14. 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.

Solution: Let a be the area of cross section and v be the velocity of water.

According to the equation of continuity, av= constant or, v α 1/a .

It means the larger the area of cross section; the smaller will be the velocity of liquid and vice versa.

Thus, as the water comes out of the vertical pipe, its velocity increases and area of cross section decreases.

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

Solution: According to the equation of continuity, if the exit hole of the pipe is partially closed, the water stream comes out with more velocity due to decrease in area. This results in the water stream going to larger distance.

16. A Gipsy car has a canvass top. When the car runs at high speed, the top bulges out. Explain.

Solution: This can be explained through Bernoulli’s principle, which states that the higher the air speed, the lower the pressure in that area. Because the air inside the car does not move, the pressure in the car is atmospheric. Because air moves outside the car (directly above it), the pressure is low. The canvas top of the Gipsy car is pushed upwards because the pressure inside the car is greater than the pressure directly above the car.

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