Question

A very large tank is filled to a depth of 250 cm with oil that has a density of 860 kg/m3 and a viscosity of 0.180 Pa · s. The base of the tank is made of a material that is 5.00 cm thick and a hole is drilled through the base with a radius of 0.750 cm. The tank is open to the air at the top. What is the initial volume flow rate of the oil through the hole?

Answer 1

According to Bernoulli's equation

P1 + (1/2)ρ * v1^2 + ρ * g * h1 = P2 + (1/2)ρ *v2^2 + ρ * g * h2

P1 = P2 = 0

or ρ * g * (h2 - h1) = (1/2)ρ * (v1^2 - v2^2)

or g * (h2 - h1) = (1/2) * v1^2 * (1 - (v2/v1)^2)--------------(1)

According to continuity equation

A1 * v1 = A2 * v2

or (v2/v1) = (A1/A2) ----------------(2)

from (1) and (2)

g * (h2 - h1) = (1/2) * v1^2 * (1 - (A1/A2)^2)

or v1 = [2g * (h2 - h1)/(1 - (A1/A2)^2)]

g = 9.8 m/s^2

(h2 - h1) = 250 cm = 250 * 10^-2 m

A1 = 2π * R * L

A2 = π * r^2

R = 5.00 cm = 5.00 * 10^-2 m

L = 250 cm = 250 * 10^-2 m

r = 0.750 cm = 0.750 * 10^-2 m