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If there is no flow the pressure before and after the neck will be the same. The faster the fluid flow, the greater the pressure difference before and after the neck. This is known as a Venturi valve. Figure 23.23 shows a Venturi valve being used to measure a fluid flow rate. The fluid flow rate will be proportional to the pressure difference before and at the neck (or after the neck) of the valve.

Figure 23.23 A Venturi Valve

continuous sensors -23.23

Aside: Bernoulli’s equation can be used to relate the pressure drop in a venturi valve.

p + -- + gz = C

where,

p = pressure ?= density v = velocity

g = gravitational constant

z = height above a reference

C = constant Consider the centerline of the fluid flow through the valve. Assume the fluid is incompressible, so the density does not change. And, assume that the center line of the valve does not change. This gives us a simpler equation, as shown below, that relates the velocity and pressure before and after it is compressed.

pbefore vbefore pafter vafter

-------------- + ------------------+ gz = C = ------------+ --------------+ gz

?2 ?2 22

pbefore vbefore pafter vafter

----------------+ ---------------- = ------------+ ------------

?2 ?2 22

vafter

? vbefore

– ------------ – --------------- ?

pbefore pafter = ?? 2

The flow velocity v in the valve will be larger than the velocity in the larger pipe section before.

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