I have a closed tank containing some liquid. At the bottom of the tank, a hole of some area is made. The liquid starts draining out, obviously at a varying rate. I would like to estimate the time needed for all the liquid to flow out of the tank. How to solve this problem using CFD?

The height and density of the liquid is known. The total volume and mass of liquid can be easily found too. The cross-sectiional area of the hole is known. Bernoulli's equation seems to be appropriate because the flow seems to be incompressible. If you find the mass flow rate of the liquid then you can easily find out how long it should take for the tank to become empty. Please note that velocity of the liquid leaving the hole as well as mass flow rate of liquid decreases as the height of the liquid starts decreasing.

One way of solving this problem is using both the Energy (Bernouilli) Equation and the Continuity Equation. Assume that state 1 is at the center of the hole at the bottom of the tank, and that state 2 is at the middle of the top surface of the liquid. Assuming that the pressure at the top of the liquid is zero gauge, ie. atmospheric, as well as the pressure of the liquid exiting at the bottom, these terms are cancelled from the energy equation. By placing your elevation datum at the bottom of the tank, z1 is zero. This leaves you with: v1^2/(2g)=v2^2/(2g)+z2. The velocities are related through the continuity equation: rho1*A1*v1=rho2*A2*v2. Since the fluid is incompressible, rho1=rho2, leaving A1*v1=A2*v2 Furthermore, v2=d(z2)/dt. Substitution leads to the following non-linear ordinary differential equation: (1-(A2/A1)^2)*(dz/dt)^2+2*g*z=0., which can be solved in any number of ways.

If you need more help or this is unclear, email me.

(1). If the tank is closed, you may have difficulty to drain the liquid inside. The water will drip from the bottom hole, but it will take forever (almost) to drain the tank. (2). For the classical theory to work, you need to drill a hole on the top of the tank first. Otherwise, the vacuum will be created in the upper part of the tank, and it will prevent the liquid to flow through the bottom hole. (3). The answer is: a) without the top hole, it will take forever to drain the tank ( in theory), b). with a top hole, the classical theory applies.