Solve Open Tank Fluid Question: Time to Empty Half Tank

[nick_gao]

question:(a little bit tricky)
A cylindrical open tank needs cleaning. The tank is filled with water to a height meter, so you decide to empty it by letting the water flow steadily from an opening at the side of the tank, located near the bottom. The cross-sectional area of the tank is square meters, while that of the opening is square meters.

How much time does it take to empty half the tank? Express your answer numerically in seconds. Take the free-fall acceleration due to gravity to be meters per second per second.

anyone can help me solve this question thank you a lot!

 

[tankFan86]

Sounds like a standard problem in ODEs. Could you be doing homework?

If you are going to solve it with ODE's, use Torricelli's law for the velocity of the jet and derive an ODE for the level of the fluid from the law of mass balance.

If you want to use PDE's, you're guess is as good as mine.

 

[nick_gao]

a little bit complicated to understant that. also i don't know what is PDE?

 

[nasu]

"The cross-sectional area of the tank is square meters, while that of the opening is square meters."

Is this some typo or maybe the dimensions are secret and were cut by the censor?
If the opening is small compared with the area of the tube, the flow is probably laminar and the speed of the jet is v=sqrt(2gh), i think.
Then the fluid flow is A*v = d(volume)/dt
d(volume)= density*g*dh
Plug in the speed and integrate to find h(t).