## Question

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/m^{3}, 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.

### Solution

4095 N/m^{2}, 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 *v*_{1} and *v*_{2} 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.

#### SIMILAR QUESTIONS

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.

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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/s^{2} 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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Water is flowing through two horizontal pipes of different diameters which are connected together. In the first pipe the speed of water is 4.0 m/s and the pressure is . Calculate the speed and pressure of water in the second pipe. The diameters of the pipes are 3.0 cm and 6.0 cm respectively.

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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/cm^{3} 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/s^{2})