Liquid Flow from Containers - Emptying Time
Calculate liquid velocity, volume flow and draining time when emptying a container.
Base Apertures
The liquid outlet velocity when draining a tank or a container can be calculated
v = Cv (2 g H )1/2 (1a)
where
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)
where
V = volume flow (m3/s)
A = area of aperture - flow outlet (m2)
Cd = discharge coefficient
where
Cd = Cc Cv
where
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)
where
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)
where
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)
where
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)
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
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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.
