A cylindrical tank with length 5 ft and raduis of 3 ft is situated wit its axis horizontal. if a circular bottom hole with a radius of 1 in. is opened and the tank is initially half full of xylene, how long will it ake for the liquid to drain completely? PLEASE HELP
3 answers
Start with Bernoulli's equation which relates dV/dt to pressure. Yes, you will have to know density of xylene. http://www.princeton.edu/~asmits/Bicycle_web/Bernoulli.html
This didn't help me much bobpursley, I am just so confused.
Write an equation (based on Bernoulli's equation) for the volume flow rate in terms of the height of the water in the tank, which is proportional to pressure. That height y will be a function of the remaining volume, V.
Derive the equation dV/dt = f{y(V)}
where y is the height of water in the tank. To get the time to empty the tank, solve by separation of variables.
Integral of t = Integral of dV/f(V)
dV/dt = -(hole area)*(liquid velocity at opening)
liquid velocity at opening= sqrt(2gy)
it appears that the liquid density cancels out. You will need to express y in terms of V to do the integration. The integration might be messy. That is as far as I am going with this.
Derive the equation dV/dt = f{y(V)}
where y is the height of water in the tank. To get the time to empty the tank, solve by separation of variables.
Integral of t = Integral of dV/f(V)
dV/dt = -(hole area)*(liquid velocity at opening)
liquid velocity at opening= sqrt(2gy)
it appears that the liquid density cancels out. You will need to express y in terms of V to do the integration. The integration might be messy. That is as far as I am going with this.
0 answers