In the mass flow rate equation shown, what does hL represent?

• A. Height between the hole in the tank and the top of the liquid
• B. Height of the tank
• C. Liquid density
• D. Height between the bottom of the tank and the hole

Answer: (A)

The mass flow through a hole in a tank is driven by the hydrostatic head of liquid above the hole. That head, h_L, is the vertical distance from the liquid surface down to the hole. It sets the pressure at the hole (p = ρ g h_L) and, via v = sqrt(2 g h_L), determines the velocity and thus the mass flow rate ṁ = ρ A v. So h_L is exactly the height between the hole and the top surface of the liquid. The other descriptions don’t represent the driving head: it’s not simply the tank’s overall height, nor the liquid’s density, nor the distance from the bottom to the hole.