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Glycerine flows steadily through a horizontal tube of length 1.5 m and radius 1.0 cm. 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 × 10^(–3)` 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
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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^(–1)` and 63 m `s^(–1)` respectively. What is the lift on the wing if its area is 2.5 `m^2` ? Take the density of air to be 1.3 kg
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Figures (a) and (b) refer to the steady flow of a (non-viscous) liquid. Which of the two figures is incorrect ? Why ?
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The cylindrical tube of a spray pump has a cross-section of 8.0 `cm^2` 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 mi`n^(–1)`, what is the speed of ejection of the liquid through the holes
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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
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Figure (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.
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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 × 10^5` Pa. Also give the excess pressure inside the
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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 40.0 cm 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 × 10^5`
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A tank with a square base of area 1.0 `m^2` is divided by a vertical partition in the middle. The bottom of the partition has a small-hinged door of area 20 `cm^2`. The tank is filled with water in one compartment, and an acid (of relative density 1.7) in the other, both to a height of 4.0 m. compute the force necessary to keep the door
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A manometer reads the pressure of a gas in an enclosure as shown in Fig. (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 76 cm 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
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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
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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
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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
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(a) What is the largest average velocity of blood flow in an artery of radius `2×10^(–3)`m if the flow must remain lanimar? (b) What is the corresponding flow rate ? (Take viscosity of blood to be 2.084 × 10–3 Pa
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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 × 10^3` kg `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
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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 × 10^3` kg
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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^(–2)` N `m^(–1)`. Take the angle of contact to be zero and density of water to be `1.0 × 10^3` kg `m^(–3)` (g = 9.8 m
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(a) It is known that density ρ of air decreases with height y as `ρ = ρ_0e^((-y)/y_0)` where `ρ_0`= 1.25 kg `m^(–3)` is the density at sea level, and `y_0` is a constant. This density variation is called the law of atmospheres. Obtain this law assuming that the temperature of atmosphere remains a constant (isothermal conditions). Also assume that the value of g remains constant. (b) A large He balloon of volume 1425 `m^3` is used to lift a payload of 400 kg. Assume that the balloon maintains constant radius as it rises. How high does it rise ? [Take
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A structural steel rod has a radius of 10 mm and a length of 1.0 m. A 100 kN force stretches it along its length.Calculate (a) stress, (b) elongation, and (c) strain on the rod. Young’s modulus, of structural steel is `2.0 × 10^(11)` N
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A copper wire of length 2.2 m and a steel wire of length 1.6 m, both of diameter 3.0 mm, are connected end to end. When stretched by a load, the net elongation is found to be 0.70 mm. Obtain the load
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