The fresh water behind a reservoir dam is 15 m deep. A horizontal pipe 4.0 cm in diameter passes through the dam 6.0 m below the water surface as shown in figure. A plug secures the pipe opening. The plug is removed. What volume of water flows out of the pipe in 3.0- hour?
As the velocity of efflux,
so assuming the level of water in the tank to be constant [(i.e,, area = ∞) as it is not given] the volume coming out per second will be
So the volume of the water flowing through the pipe in 3 hour
The density of air in atmosphere decreases with height and can be expressed by the relation:
Where is the density at sea-level, A is a constant and h is the height. Calculate the atmospheric pressure at sea-level. Assume g to be constant.
A rod of length 6 m has a mass 12 kg. It is hinged at one end at a distance of 3 m below water surface. (a) What weight must be attached to the other end of the rod so that 5 m of the rod are submerged? (b) Find the magnitude and direction of the force exerted by the hinge on the rod.
(Specific gravity of rod is 0.5).
A large block of ice 5 m thick has a vertical hole drilled through it floating in the middle of a lake. What is the minimum length of a rope required to scoop up a bucket full of water through the hole?
[RD of ice = 0.9]
A cubical block of iron 5 cm on each side is floating on mercury in a vessel. Water is poured into the vessel so that it just covers the iron block. What is the height of water column?
[RD of Hg = 13.6 and Fe = 7.2]
A glass beaker having mass 390 g and an interior volume of 500 cm3 floats on water when it is less than half filled with water. What is the density of the material of the beaker?
A block of wood weighs 12 kg and has a relative density 0.6. It is to be in water with 0.9 of its volume immersed. What weight of a metal is needed if the metal is attached below the wood?
[RD of metal = 14]
A wooden stick of length L, radius R and density has a small metal piece of mass m (of negligible volume) attached to its one end. Find the minimum value of the mass m (in terms of given parameters) that would make the stick float vertically in equilibrium in a liquid of density .
Calculate the rate of flow of glycerine of density through the conical section of a pipe, if the radii of its ends are 0.1 m and 0.04 m and the pressure drop across its length is 10 N/m2.
A non-viscous liquid of constant density 1000 kg/m3 flows in a streamline motion along a tube of variable cross-section. The tube is kept inclined in the vertical plane as shown in figure. The area of cross-section of the tube at two points P and Q at heights of 2 metre and 5 metre are respectively the velocity of the liquid at point P is 1 m/s. Find the work done per unit volume by the pressure and the gravity forces as the fluid flows from point P to Q.
A soap film is on a rectangular wire ring of size . If the size of the film is changed to , then calculate the work done in this process. The surface tension of soap film is .