Fluid Flow
Fluid Flow
(OP)
A Styrofoam cylinder, filled with water, sits on a table. You then poke a small hole through the side of the cylinder, 20 cm below the top of the water surface. What is the speed of the fluid emerging from the hole? Thank you.
RE: Fluid Flow
- Andrew
RE: Fluid Flow
To simplify, I would convert potential energy at the hole, assuming the hole was recently put into the container and the water level has not yet dropped, and then convert to kinetic energy to solve for fluid velocity. This can be achieved using Bernouilli's equation, and is a classic question in basic fluid dynamic coursework.
RE: Fluid Flow
RE: Fluid Flow
Bernoulli -> Toricelli:
p1 + rho*g*h1 + 1/2*rho*v1^2 = p2 +rho*g*h2 + 1/2*rho*v2^2
p1 = p2 = patm
h1 = 0.2 m
h2 = 0 m
A1*v1 = A2*v2 -> A1 >> A2 -> v1 << v2 and v1 = 0 m/s
=>
rho*g*h1 = 1/2*rho*v2^2
-> sqrt(2*g*h1) = v2 (Toricelli)
with h1 = 0.2 m
-> v2 = sqrt(2*9.81*0.2) = 1.98 m/s