Question

A cylindrical tank of radius R is filled with a liquid of density  to a height H above its bottom. It has a small hole of radius r in the mantle at distance h above its bottom. Air pressure equals p0. You are to use Bernoulli’s equation to compute the flow velocity of the fluid as it exits the hole. a) Prepare a diagram. Indicate the location of the two points that you choose when applying Bernoulli’s equation. What are the pressures at those points? Hint: Consult example 14.12 in Knight. b) Derive an expression for the velocity v of the liquid emerging from the hole in terms of p0, , r, R, h, H. Assume r << R, hence (at the top of the container) v1 ≈ 0. c) Compute v if the liquid is water, p0 = 1 atm, R = 20 cm, r = 1 mm, H = 80 cm, h = 30 cm.

Answer 1