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].
Does it matter if one uses gauge instead of absolute pressures in applying Bernoulli’s equation ? Explain.
Can Bernoulli’s equation be used to describe the flow of water through a rapid in a river ? Explain.
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