Question

The faucet at the bottom of a large tank holding gasoline is 1.2m above the ground. The top surface of gasoline in the tank is 3.6m above the faucet. The pressure at the top of the tank is atmospheric pressure. Assuming that the area of the tank is much greater than the area of the faucet determine the speed with which the gasoline leaves the faucet.

Answer 1

By applying Bernoulli's theroem at faucet and top of tank,

P1 + 0.5*rho*v1^2 + rho*g*h1 = P2 + 0.5*rho*v2^2 + rho*g*h2

here,

rho = density of gasoline = 748.9 kg/m^3

h1 - h2 = 3.6 m

v1 = 0 m/sec (Since area of tank is larger than area of faucet)

v2 = ?

P1 = P2 = Atmospheric pressure

So, 0.5*rho*v2^2 = rho*g*(h1 - h2)

v2 = sqrt(2*g*(h1 - h2))

v2 = sqrt(2*9.8*3.6)

v2 = 8.4 m/sec.

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