Air is streaming past a horizontal aeroplane wing such that its speed is 120 ms–1 at the upper surface and 90 ms–1 at the lower surface. If the density of air is 1.3 kg/m3, find the difference in pressures between the two surfaces of the wing. If the wing is 10 m long and has an average width of 2 m, then calculate the gross lift on it.
4095 N/m2, 81900 N
By the principle of continuity and the Bernoulli’s theorem, the difference in pressure between the upper and the lower surface of the aeroplane wing is
Here v1 and v2 are speeds of air streams at upper and lower surface respectively, and is density of air.
Substituting the values :
If the area of the wing is A, then the gross lift on it is
= 81900 N.
A metal sphere of diameter enters water after falling a distance h freely in the gravitational field of the earth. After entrance in water, its velocity remains unchanged. Calculate the value of h. The coefficient of viscosity of water , density of water and acceleration due to gravity = 10 N/kg.
An air bubble of radius 1.0 mm rises with uniform velocity through a viscous liquid of density 1625 kg/m3. Calculate the velocity of the bubble if the coefficient of viscosity of the liquid is 10 poise and the density of air is negligible. (g = 10 m/s2).
An air bubble of radius 0.1 mm is moving upwards in water with a velocity of 0.35 cm/s. If the density of water is and gravitational acceleration is 9.8 m/s2 and the density of the air is negligible, then find out the coefficient of viscosity of water.
A small sphere falls from rest under gravity in a viscous medium, producing heat due to friction. Find how rate of production of heat does depend upon the radius of the sphere at terminal velocity.
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A liquid is kept in a cylindrical vessel which is being rotated about its axis. The liquid rises at the sides. If the radius of the vessel is 0.05 m and the speed of rotation is 2 rev/s, find the difference in the heights of liquid at the centre of the vessel and at its sides.
The pressure difference between two points along a horizontal pipe, through which water is flowing, is 1.4 cm of mercury. If, due to non-uniform cross-section, the speed of flow of water at the point of greater cross-section is 60 cm/s, calculate the speed at the other point. Density of mercury .
Water flows into a horizontal pipe whose one end is closed with a valve and the reading of a pressure gauge attached to the pipe is . This reading of the pressure gauge falls to when the valve is opened. Calculate the speed of water flowing into the pipe.
A horizontal tube has different cross-sectional areas at points A and B. The diameter of A is 4 cm and that of B is 2 cm. Two manometer limbs are attached at A and B. When a liquid of density 0.8 g/cm3 flows through the tube, the pressure-difference between the limbs of the manometer is 8 cm. calculate the rate of flow of the liquid in the tube. (g = 980 cm/s2)