# Flow of Liquids from Containers - Volume Flow and Emptying Time Calculator

## Liquid velocity, volume flow and draining time when emptying containers

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### Base Apertures

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

*v = C _{v} (2 g H )^{1/2} (1a) *

*where *

*v = outlet velocity (m/s)*

*C _{v} = velocity coefficient (water 0.97)*

*g = acceleration of gravity (9.81 m/s ^{2})*

*H = height (m)*

The liquid** volume flow** can be calculated

*V = C _{d} A (2 g H)^{1/2} (1b)*

*where *

*V = volume flow (m ^{3}/s)*

*A = area of aperture - flow outlet (m ^{2})*

*C _{d} = discharge coefficient *

*where *

*C _{d} = C_{c} C_{v} *

*where *

*C _{c} = contraction coefficient (sharp edge aperture 0.62, well rounded aperture 0.97)*

*A = area aperture (m ^{2})*

#### 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

*C _{d} = 0.62 0.97*

* = 0.6*

The are of the aperture can be calculated as

*A = π ((0.1 m) / 2) ^{2}*

* = 0.008 m ^{2}*

The volume flow through the aperture can be calculated as

*V = 0.6 _{ }(0.008 m^{2}) (2 (9.81 m/s^{2}) (3 m))^{1/2} *

* = 0.037 m ^{3}/s*

For height *1.5 m* the volume flow is *0.1 m ^{3}/s*. For height

*0.5 m*the volume flow is

*0.06 m*.

^{3}/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.

* Bottom area of tank or container (m ^{2})*

* H - height between surface and aperture (m)*

* A - aperture area (m ^{2})*

* C _{d} - discharge coefficient*

* no. of "slices" (for the iterative calculation)*

- 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 = C _{v} (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 = C _{d} A (2 g H)^{1/2} (2c)*

**Reaction force** can be expressed as

*F = ρ V v (2d)*

*where *

*ρ = density (kg/m ^{3}) (water 1000 kg/m^{3})*

### Large Lateral Apertures

**Volume flow** can be expressed as

*V = 2/3 C _{d} b (2 g)^{1/2} (H_{2}^{3/2} - H_{1}^{3/2}) (3a) *

*where *

*b = width of aperture (m)*

### Excess Pressure in Container

**Outlet velocity** can be expressed as

*v = C _{v} (2 (g H + p / ρ))^{1/2} (4a)*

*where *

*p = excess pressure in container or tank (N/m ^{2}, Pa)*

**Volume flow** can be expressed as

*V = C _{d} A (2 (g H + p / ρ))^{1/2} (4b) *

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