A basic laboratory setup is shown in Fig. 10.17 for the pur-poses of studying flow in a stenotic artery. Determine the inlet pressure for the test section.

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Accepted Answer

Here, we must use the pipe-flow equation separately for the upstream and downstream sections relative to the test section. For the upstream section (assuming a steady laminar flow; i.e., [latex]Re\lt2,100[/latex]), we have

[latex] \left(\frac{p_{1}}{ ho }+gh+\frac{1}{2}(2)\overline{ u }^{2}_{1} ight)-\left(\frac{p_{3}}{ ho }+\frac{1}{2}(2)\overline{ u }^{2}_{3} ight)[/latex]

[latex] =\frac{64}{Re}\left(\frac{L_{1}+L_{2}}{D} ight)\frac{\overline{ u }^{2} }{2}+\sum{(K_{entrance}+K_{bend})\frac{\overline{ u }^{2} }{2} }.[/latex]

If the reservoir is open to atmosphere [latex]p_{1}=0[/latex] (gauge) and if the reservoir is large, then [latex]\overline{ u }_{1}\ll \overline{ u }_{3}.[/latex] Hence, we have

[latex] p_{3}= ho gh-\frac{1}{2} ho \overline{ u }^{2}(2+K_{e}+K_{b})-\frac{32\mu \overline{ u } }{D^{2}}(L_{1}+L_{2}).[/latex]

A similar downstream analysis will provide the value of [latex]p_{4}.[/latex] FIGURE 10.17 Possible laboratory setup to examine flow through a stenotic vessel.

Question 10.10: A basic laboratory setup is shown in Fig. 10.17 for the pur-...

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