A large tank, open at the top, is partially filled with water (1000 kg/m^3). The

Question

A large tank, open at the top, is partially filled with water (1000 kg/m^3). The tank is fitted with a spout located at a distance Deltaz =3.2 m below the surface. The spout has a diameter D = 4.0 cm and initially it is sealed with a removable tightly fitting metal disk, (a) Find the net force on the disk, (b) By the action of a lever, the disk is then removed, thereby allowing for the water to spill out. Find the speed v with which water pours out of the tank and the corresponding volume flow rate. The atmospheric pressure is 1.01 times 10^5 Pa.

Explanation / Answer

here,

D = 4 m

radius , r = 2 m

density of water , p = 1000 kg/m^3

dZ = 3.2 m

(a)

the net force on the disk , F = p * g * dZ * area

F = p * g * dZ * pi * r^2

F = 1000 * 9.8 * 3.2 * pi * 2^2

F = 3.94 * 10^5 N

(b)

the speed , v = sqrt(2 * g * dZ)

v = sqrt( 2 * 9.8 * 3.2 )

v = 7.92 m/s

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