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Liquid Flow from Containers - Emptying Time

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Base Apertures


The liquid outlet velocity when draining a tank or a container can be calculated

v = Cv (2 g H )1/2                                (1a)


v = outlet velocity (m/s)

Cv = velocity coefficient (water 0.97)

g = acceleration of gravity (9.81 m/s2)

H = height (m)

The liquid volume flow can be calculated

V = Cd A (2 g H)1/2                        (1b)


V = volume flow (m3/s)

A = area of aperture - flow outlet (m2)

Cd = discharge coefficient


Cd = Cc Cv 


Cc = contraction coefficient (sharp edge aperture 0.62, well rounded aperture 0.97)

A = area aperture (m2)

Example - Volume Flow when draining a Container

The height from the surface to the outlet aperture in a water filled container is 3 m. The aperture is sharp edged with diameter 0.1 m. The discharge coefficient can be calculated as

Cd = 0.62 0.97

     = 0.6

The area of the aperture can be calculated as

A = π ((0.1 m) / 2)2

   =   0.008 m2

The volume flow through the aperture can be calculated as

V = 0.6(0.008 m2) (2 (9.81 m/s2) (3 m))1/2  

   = 0.037 m3/s

For height 1.5 m the volume flow is 0.026 m3/s. For height 0.5 m the volume flow is 0.015 m3/s.

Draining Tank Calculator

This calculator is based on eq. (1b) and can be used to estimate the volume flow and time used to drain a container or tank through an aperture.

The calculator divides the container in "slices" and makes an iterative average calculation for each slice. The accuracy of the calculation can be increased by increasing the number of slices.

- results in table below!

Note! - the flow is reduced and the time is increased with reduced height.

Small Lateral Apertures

Outlet velocity can be expressed as

v = Cv (2 g H)1/2                                (2a)

Distance s can be expressed as

s = 2 (H h)1/2                               (2b)

Volume flow can be expressed as

V = Cd A (2 g H)1/2                             (2c)

Reaction force can be expressed as

F = ρ V v                                 (2d)


ρ = density (kg/m3)  (water 1000 kg/m3)

Large Lateral Apertures

Volume flow can be expressed as

V = 2/3 Cd b (2 g)1/2 (H23/2 - H13/2)                                (3a)


b = width of aperture (m)


Excess Pressure in Container

Outlet velocity can be expressed as

v = Cv (2 (g H + p / ρ))1/2                               (4a)


p = excess pressure in container or tank (N/m2, Pa)

Volume flow can be expressed as

V = Cd A (2 (g H + p / ρ))1/2                           (4b)

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Related Topics

Fluid Mechanics

The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.

Related Documents

Bernoulli Equation

Conservation of energy in a non-viscous, incompressible fluid at steady flow.

Cylindrical Tanks - Volumes

Volume in US gallons and liters.

Mechanical Energy Equation vs. Bernoulli Equation

The Mechanical Energy Equation compared to the Extended Bernoulli Equation.

Open Horizontal Pipes - Discharge Length vs. Volume Flow

Discharge length vs. volume flow from water filled horizontal pipes.

Orifice, Nozzle and Venturi Flow Rate Meters

The orifice, nozzle and venturi flow rate meters makes the use of the Bernoulli Equation to calculate fluid flow rate using pressure difference through obstructions in the flow.

Vertical Pipes - Discharge Height vs. Volume Flow

Volume flow and discharge height from vertical water pipes.

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