In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the lower and upper surfaces of the wing are v and respectively. If the density of air is and the surface area of the wing is A, the dynamic lift on the wing is given by
Let p1 and p2 be the air pressures on the upper and lower surfaces of the wing. Then from Bernoulli’s theorem we have
where . Therefore, the pressure difference is
Force of dynamic lift = pressure difference surface area of wing
A common hydrometer has a uniform stem graduated downwards from 0, 1, 2, ….. up to 10. When floating in pure water it reads 0 and in a liquid of relative density 1.5, it reads 10. What is the relative density of a liquid in which it reads 5?
A piece of ice, with a stone frozen inside it, is floating in water contained in a beaker. When the ice melts, the level of water in the beaker
A cubical vessel of height 1 m is full of water. What is the amount of work done is pumping water out of the vessel? Take g = 10ms–2
The dimensions of viscosity in terms of M, L and T are
The dimensions of Reynold’s number are
A rain drop of radius r falls in air with a terminal speed vt. What is the terminal speed of a rain drop of radius 2r?
Eight spherical rain drops of the same mass and radius are falling down a terminal speed of 6 cms–1. If they coalesce to form one big drop, what will be its terminal speed? Neglect the buoyancy due to air.
Water flows steadily through a horizontal pipe of a variable cross-section. If the pressure of water is p at a point where the velocity of flow is v, what is the pressure at another point where the velocity of flow is 2v; being the density of water?
The cylindrical tube of a spray pump has a radius R, one end of which hasn fine holes, each of radius r. If the speed of flow of the liquid in the tube is V, the speed of ejection of the liquid through the holes is
A piece of copper having an internal cavity weights 264 g in air and 221 g in water. The density of copper is 8.8 gm–3. What is the volume of the cavity?