A basic understanding of engineering and mathematics is necessary to calculate the time required to empty a cylindrical or rectangular water tank.
With this Excel sheet, none is required. Simply input the parameters:
- Diameter / Length and Width of the tank
- Depth of the tank
- Size of the hole/orifice
The sheet will calculate:
- The time required to fully empty the tank.
- The time needed to reach a specific water depth.
These calculations are based on a formula derived from Bernoulli’s equation. The derived formula is:
Here’s the Excel sheet. Just enter the input in YELLOW. Get the desired output.
Now, let’s also look into the theory of it.
The equation is derived based on Bernoulli’s equation, where continuity of flow is considered.
Volume reduced in tank = Volume out from hole (per unit time)
where,
- Cv is the coefficient of discharge
- Ao is Area of Hole
- g is acceleration due to gravity
- H is the depth of the Tank
Rearranging the equation, we get,
Integrating it,
Solving it, we finally get:
The above equation can solve both the time to empty the full tank and also to reach the desired decrease in depth.
For the time to empty the full tank, the H1 is simply Zero (0).
