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## Main Question or Discussion Point

Hello everyone,

Say I have a closed loop comprised of a pump and some piping which connects the inlet of the pump to the outlet of the pump. All of the piping has radius "a," except for a small section, which constricts to radius "b" for a small portion of the line (the inlet and outlet connections are both of radius "a"). Neglecting friction, is there any pressure drop between the inlet and the outlet of the pump if an incompressible fluid were to flow through the system at some flow rate? If so, does Bernoulli's principle in the following fashion account for the magnitude of the pressure drop?

dP = | 1/2*(fluid density)*(flow rate)^2*(1/(pi*a^2)^2-1/(pi*b^2)^2) |

I used (flow rate) = (cross sectional area)*(flow speed) to express the flow speeds, and the fact that the flow rate is the same.

Here it is in TeX form:

[tex] \Delta P = \frac{1}{2} \rho Q^2 \left( (\frac{1}{\pi a^2})^2 - (\frac{1}{\pi b^2})^2 \right) [/tex]

Thanks for your help and time,

F2

Say I have a closed loop comprised of a pump and some piping which connects the inlet of the pump to the outlet of the pump. All of the piping has radius "a," except for a small section, which constricts to radius "b" for a small portion of the line (the inlet and outlet connections are both of radius "a"). Neglecting friction, is there any pressure drop between the inlet and the outlet of the pump if an incompressible fluid were to flow through the system at some flow rate? If so, does Bernoulli's principle in the following fashion account for the magnitude of the pressure drop?

dP = | 1/2*(fluid density)*(flow rate)^2*(1/(pi*a^2)^2-1/(pi*b^2)^2) |

I used (flow rate) = (cross sectional area)*(flow speed) to express the flow speeds, and the fact that the flow rate is the same.

Here it is in TeX form:

[tex] \Delta P = \frac{1}{2} \rho Q^2 \left( (\frac{1}{\pi a^2})^2 - (\frac{1}{\pi b^2})^2 \right) [/tex]

Thanks for your help and time,

F2

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