Orifice meter and Venturi meter: Any kind of energy loss?

When an incompressible fluid flows through a pipe since it does not do any thermodynamic work, H = U + W, and W =0, H or the total energy of the fluid is equal to the internal energy of the fluid. The fluid only switches energy between kinetic and potential energies with no loss of total energy.

Flow meters in the form of contraction devices like orifice meters are the most common. Here, differential pressure is created by converting part of the potential energy of the flow [static pressure] into kinetic energy by changing the cross-section of the pipeline. The difference (Δp) between the pressure upstream of the contraction device (P-in) and the pressure downstream of the device (P-out) is related to the flow rate by, M = αS √[2 ρ Δp], where S is the cross-sectional area of the channel upstream of the meter and α is a characteristic coefficient. Ρ is the density.

What is static pressure:

According to Bernoulli’s equation,

V1^2/2g + P1/ rho + Z = V2^2/2g + P2/ rho + Z = Total energy

Ignore, elevation effect = Z

Then at rest, the total energy of a fluid is its static pressure energy P/ rho. This is the fluid’s internal energy which is the fluid’s total energy with which it starts its journey.

What is Δp?

At constant elevation, Δp is proportional to the differential kinetic energy up and downstream the fluid supplies from its internal energy.

How does the orifice meter work?

An orifice meter consists of a flat plate that has a sharp-edged hole accurately machined in it and placed concentrically in a pipe as shown above. As liquid flows through the pipe, the flow suddenly contracts as it approaches the orifice and then suddenly expands after the orifice back to the full pipe diameter. This forms a vena contracta or a throat immediately past the orifice. This reduction in flow pattern at the vena contracta causes increased velocity and hence lower pressure at the throat.

Because of the abrupt contraction and expansion, the fluid past the orifice cannot recover its initial kinetic energy and that causes a decrease in the flow rate. But total energy remains constant as explained the total energy is conserved and the total energy in the absence of any thermodynamic work is its internal energy. No energy goes anywhere.

Orifice meter for gases

The fundamentals remain the same two things are different [1] the density changes and [2] gas does thermodynamic work as the gas expands by using its internal energy. Both depend on the Cp/Cv of the gas. The difference (Δp) between the pressure upstream of the contraction device (P-in) and the pressure downstream of the device (P-out) is related to the flow rate by, M = αS √[2 ρ Δp], where S is the cross-sectional area of the channel upstream of the meter and α is a characteristic coefficient. Ρ is the density.

Cv [specific heat at constant volume] becomes the decision maker. Larger the molecular mass of the gas the larger the number of degrees of freedom and therefore the larger Cv or internal energy or the smaller the kinetic energy recovery past the orifice and vice-versa.

To summarize, the total energy as the liquid flows remains constant what happens is past the orifice due to abrupt contraction and expansion the system cannot recover its original kinetic energy and that accounts for the smaller characteristic coefficient.

Venturi meter

It comprises a cylindrical inlet section followed by a convergent entrance into a cylindrical throat and a divergent outlet section.

How does it work

The venturi meter consists of a smooth gradual contraction from the main pipe size to the throat section, followed by a smooth, gradual enlargement from the throat section to the original pipe diameter.

The included angle from the main pipe to the throat section in the gradual contraction is generally in the range of 21° ± 2°. Similarly, the gradual expansion from the throat to the main pipe section is limited to a range of 5° to 15° in this design of the venturi meter. This construction results in minimum energy loss, causing the discharge coefficient to approach the value of 1.0 the reason being a much larger recovery of kinetic energy past the orifice.

Credit: Google