Two vessels have the same base area but different shapes. The first vessel takes twice the volume of water that the second vessel requires to fill upto a particular common height. Is the force exerted by the water on the base of the vessel the same in the two cases ? If so, why do the vessels filled with water to that same height give different readings on a weighing scale ?
A manometer reads the pressure of a gas in an enclosure as shown in Fig. 10.25 (a)When a pump removes some of the gas, the manometer reads as in Fig. 10.25 (b)The liquid used in the manometers is mercury and the atmospheric pressure is 76cm of mercury.
(a) Give the absolute and gauge pressure of the gas in the enclosure for cases (a)
and (b), in units of cm of mercury.
(b) How would the levels change in case (b) if 13.6 cm of water (immiscible with
mercury) are poured into the right limb of the manometer ? (Ignore the small
change in the volume of the gas).
What is the excess pressure inside a bubble of soap solution of radius 5.00 mm, given that the surface tension of soap solution at the temperature (20 °C) is 2.50 ×10–² N m–¹ ? If an air bubble of the same dimension were formed at depth of 40.0cm inside a container containing the soap solution (of relative density 1.20), what would be the pressure inside the bubble ? (1 atmospheric pressure is 1.01 × 10⁵ Pa).
What is the pressure inside the drop of mercury of radius 3.00 mm at room temperature ? Surface tension of mercury at that temperature (20 °C) is 4.65 ×10–¹ N m–¹. The atmospheric pressure is 1.01 × 10⁵ Pa. Also give the excess pressure inside the drop.
Figure 10.24 (a) shows a thin liquid film supporting a small weight = 4.5 × 10–2 N. What is the weight supported by a film of the same liquid at the same temperature in Fig. (b) and (c) ? Explain your answer physically.
A U-shaped wire is dipped in a soap solution, and removed. The thin soap film
formed between the wire and the light slider supports a weight of 1.5 × 10–² N
(which includes the small weight of the slider). The length of the slider is 30 cm.
What is the surface tension of the film ?
The cylindrical tube of a spray pump has a cross-section of 8.0 cm² one end of which has 40 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is 1.5 m min–¹, what is the speed of ejection of the liquid through the holes ?
Figures 10.23(a) and (b) refer to the steady flow of a (non-viscous) liquid. Which of the two figures is incorrect ? Why ?
In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are 70 m s–¹and 63 m s-¹ respectively. What is the lift on the wing if its area is 2.5 m² ? Take the density of air to be 1.3 kg m–³.
Glycerine flows steadily through a horizontal tube of length 1.5 m and radius 1.0cm. If the amount of glycerine collected per second at one end is 4.0 × 10–³ kg s–¹, what is the pressure difference between the two ends of the tube ? (Density of glycerine = 1.3 × 103 kg m–3 and viscosity of glycerine = 0.83 Pa s). [You may also like to check if the assumption of laminar flow in the tube is correct].
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