Venturi tube flow calculation - theory
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Calculation of flow through the Venturi tube is for incompressible flow,
based on the Bernoulli principle:
where is:
p - pressure
rho - density view table
V - velocity
g - gravitational constant (9.81 m/s2)
z - geodetic height
Assumption that
pressure lost is negligible:
and:
and if velocities substituted with flow rate:
where is:
Q - volumetric flow rate
D - diameter
Pressure drop through the
Venturi tube because of velocity increase can be calculated as follows:
or:
Expressing flow rate
from the previous equation leads to:
Substituting:
flow rate can be determined as:
where C is coefficient of discharge.
The above
equation is main one used for flow calculation in
calculator.
Other values are
calculated using following equations:
mass flow:
velocities:
If the calculator is used for gas flow, then gas is
considered as incompressible and ideal. Equation for ideal gas:
can be used for calculation of temperature T:
as well as density rho:
where R is gas constant (R=287 J/kgK for air)
Coefficient of discharge C
As fluid exits a reservoir through a small hole and enters another one, or flows out to the
open air, stream lines tend to contract
itself, mostly because of inertia. Coefficient of discharge C is used to include this
effect.
For the Venturi tubes with diameters in range of D = (200 - 1200 mm), D2/D1
= (0.4 - 0.7) and ReD = (2 ·105 - 2 ·106) the coefficient
of discharge is C = 0.985.
In this calculator for coefficient off discharge C following equation has
been used:
where a, b, and c depend on the type of Venturi tube.
For welded tube, these coefficients are:
a=0.70304970
b=0.00490015
c=-0.00024547
For casted tube are:
a=0.60892370
b=0.00659844
c=-0.00033123
And for machined are:
a=0.49670179
b=0.00873339
c=-0.00044367
Reynolds number on inlet ReD is calculated using well known equation:
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