Flow through the pipe coupling (union) in Fig. 8–11 is to be studied using a scale model. The actual pipe is 100 mm in diameter, and the model will use a pipe that is 20 mm in diameter. The model will be made of the same material and transport the same fluid as the prototype. If the velocity of

Question

Flow through the pipe coupling (union) in Fig. 8–11 is to be studied using a scale model. The actual pipe is 100 mm in diameter, and the model will use a pipe that is 20 mm in diameter. The model will be made of the same material and transport the same fluid as the prototype. If the velocity of flow through the prototype is estimated to be 1.5 m/s, determine the required velocity through the model.

Accepted Answer

A relationship between the velocities and the diameters can be obtained by realizing that the forces dominating the flow are caused by inertia and viscosity, so Reynolds number similitude must be satisfied. We require

[latex] \left(\frac{ ho V D}{\mu} ight)_m=\left(\frac{ ho V D}{\mu} ight)_p [/latex] (1)

Since the same fluid is used for both cases,

[latex] \begin{gathered} V_m D_m=V_p D_p \ \ V_m=\frac{V_p D_p}{D_m}=\frac{(1.5 m / s )(100 mm )}{20 mm }=7.50 m / s \end{gathered} [/latex]

As noted, Reynolds number similitude leads to high flow velocities for the model due to this scaling factor. To lower this velocity, from Eq. 1, one can use a higher-density or lower-viscosity fluid for the model.

Question 8.5: Flow through the pipe coupling (union) in Fig. 8–11 is to be...

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