Most commonly used method for measuring flow rate is by
measuring the differential pressure across pipe restriction. Pitot tube and
Orifice are widely used to generate differential pressure in pipe line.We all know that flow rate is proportional to the square root of DP. And how that we will derive here.
To understand this fundament, we should know some basic
principles.
(1)
Bernoulli’s equation: In short, this states
that, the sum of the pressure energy
(P),
kinetic energy (½ * ρ *
V²) and potential energy (ρ * g * h) will be equal at any cross section.
P₁
+ (½ * ρ *
V₁²) + (ρ * g * h₁)
= P₁ + (½ * ρ
* V₂²)
+ (ρ * g * h₂) ………………(1)
(2)
Continuity Equation: The continuity equation
states that the mass flow through any cross section of pipe will be equal.
A₁ * V₁ = A₂ * V₂. ………………..(2)
Now, assume that
our measurement pipe is at same level. So, Potential energy term in
Bernoulli’s equation (1) will be same at both point and can be cancelled out.
P₁
+ (½ * ρ *
V₁²) = P₁ +
(½ * ρ * V₂²) …………………..(3)
From equation (2),
V₁ = (A₂ * V₂ / A₁)
V₁ = (d/D)² * V₂
Putting this in above equation (3) and solving
for V₂
…………………………..
(4)
Or we can say
…………………………..
(5)
It means differential pressure type flowmeter will be 1/2 as sensitive to changes in fluid density as a velocity type flowmeter.
This is the equation for the velocity
at the meter throat. Volumetric flow (Qv) equation can be obtained by
multiplying by the cross sectional area of the throat.
If Mass flow is required rather
than volumetric flow, multiply both the side by flowing density…
Density compensation for Eq (5) is required for accurate flow measurement, that I'll post in my next blog.
Reference: Rosemount Technical paper for flow measurement
