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Home Blog Fluid Management Pressure at the vena contracta with liquid flow in a control valve

Pressure at the vena contracta with liquid flow in a control valveWritten by Jon Monsen Thursday, 11 April 2013 11:52

I was recently asked how the pressure at the vena contracta of a control valve in a liquid application can bedetermined. I am sharing my answer below.

Here are some comments on the pressure at the vena contracta:

The Liquid Pressure Recovery Factor, published by control valve manufacturers for each of their valves, isdefined as:

Where:

P is the pressure drop across the valve (P1 P2)

P1 is the absolute pressure upstream of the valve.

PVC is the pressure at the vena contracta.

It is important to understand that this equation is only valid when the density at the vena cotracta remainsconstant. It does not apply when there is vaporization at the vena contracta.

The valve manufacturers determine the FL of their valves by increasing the pressure drop across the valve untilflow becomes fully choked

The flow vs. square root of pressure drop actually follow the blue line on the figure below, but the IEC liquidvalve sizing equations don't attempt to predict the rounded portion of the graph, but instead predict a flow vs.square root of pressure drop relationship as shown by the green and red dashed lines.

Once the test determines that flow is fully choked (the flow does not increase with increasing pressure drop),the point where the red and green lines on the figure intersect is defined as the transition point betweennon-choked flow and choked flow and is also the point that separates the IEC equation for liquid non-chokedflow from the IEC liquid equation for choked flow. The IEC does not give this point a name. I like to call it the"Terminal Pressure Drop," abbreviated PT . Others have called it various things, such as "Allowable pressuredrop" "Critical pressure drop" and "Max pressure drop," to mention a few.

The valve manufacturer then solves the IEC equation for the Choked flow point (what I call PT ) to come upwith FL.

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Pressure at the vena contracta with liquid flow in a control valve http://www.valin.com/blog/14-fluid-management-/422-pressure-at-the-...

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Where PV is the vapor pressure of the liquidand FF is the "Critical Pressure Ratio factor"

Where PC is the thermodynamic critical pressure of the liquid.Back to the question of determining the pressure at the vena contracta, you can rewrite the equation thatdefines FL in terms of the pressure at the vena contracta, PVC

This is only valid up to the point where choked flow begins. Once flow becomes choked there is vaporization atthe vena contracta and the density at the vena contracta decreases. When the density decreases, the pressurerecovery decreases. Once vaporization at the vena contracta is fully developed, the pressure at the venacontracta reaches its lower limit. If the downstream pressure is then further decreased, the result will be morevaporization, but the vena contracta pressure is not affected and the flow rate stays the same.

Most of the polished information i have seen on choked flow and cavitation is based on tests with cold water. Ihave no experience with or knowledge of the effects of solutions and mixtures of liquids, such as hydrocarbonliquids.

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Pressure at the vena contracta with liquid flow in a control valve http://www.valin.com/blog/14-fluid-management-/422-pressure-at-the-...

2 of 2 18/10/2013 17:07