Two narrow bores of diameters 3.0 mm and 6.0 mm are joined together to form
a U-tube open at both ends. If the U-tube contains water, what is the difference in its levels in the two limbs of the tube ? Surface tension of water at the temperature of the experiment is 7.3 × 10–²N m–¹. Take the angle of contact to be zero and density of water to be 1.0 × 10³ kg m–³ (g = 9.8 m s–²) .
Mercury has an angle of contact equal to 140° with soda lime glass. A narrow tube of radius 1.00 mm made of this glass is dipped in a trough containing mercury. By what amount does the mercury dip down in the tube relative to the liquid surface outside ? Surface tension of mercury at the temperature of the experiment is 0.465 N m–¹. Density of mercury = 13.6 × 10³ kg m–3
In Millikan’s oil drop experiment, what is the terminal speed of an uncharged drop of radius 2.0 × 10–⁵ m and density 1.2 × 10³kg m–³. Take the viscosity of air at the temperature of the experiment to be 1.8 × 10–5 Pa s. How much is the viscous force on the drop at that speed ? Neglect buoyancy of the drop due to air.
A plane is in level flight at constant speed and each of its two wings has an area of 25 m². If the speed of the air is 180 km/h over the lower wing and 234 km/h over the upper wing surface, determine the plane’s mass. (Take air density to be 1 kgm–³).
(a) What is the largest average velocity of blood flow in an artery of radius 2×10–³m if the flow must remain lanimar? (b) What is the corresponding flow rate ? (Take viscosity of blood to be 2.084 × 10–³ Pa s).
In deriving Bernoulli’s equation, we equated the work done on the fluid in the tube to its change in the potential and kinetic energy.
(a) What is the largest average velocity of blood flow in an artery of diameter 2 × 10–3 m if the flow must remain laminar ?
(b) Do the dissipative forces become more important as the fluid velocity increases ? Discuss qualitatively.
During blood transfusion the needle is inserted in a vein where the gauge pressure is 2000 Pa. At what height must the blood container be placed so that blood may just enter the vein ? [Use the density of whole blood from Table 10.1].
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).
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