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Discharge Time under Falling Head Formulae and Calculator

Hydraulics & Pneumatic Engineering & Design
Fluids Engineering and Design
Civil Engineering and Design

Fluid Flow Discharge Time under Falling Head Formula and Calculator

The flow from a reservoir or vessel when the inflow is less than the outflow represents a condition of falling head. The time required for a certain quantity of water to flow from a reservoir can be calculated by equating the volume of water that flows through the orifice or pipe in time dt to the volume decrease in the reservoir. If the area of the reservoir is constant,

Formula 1
t = 2 · A / [ C · a · ( 2 g )1/2 ] · ( h11/2 - h21/2 )


h1 = head at the start, ft (m)
h2 = head at the end, ft (m)
A = Surface area of reservoir or vessel, ft2 (m2)
t = time interval for head to fall from h1 to h2, s
C = coefficient of discharge
a = area of discharge orifice, ft2 (m2)
g = 32.2 ft/s2 (9.81 m/s2)