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October 18th, 2019, 07:34 AM   #1
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Exclamation bernoulli's law

The height of a funnel is 20cm if the upper diameter is 20cm and the lower diameter is 2cm find the pressure difference between two cross sectional areas if in every second 0.3L of water pass through the funnel?
I translate this question from Persian sorry if there is any grammatical mistake or misspelling
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October 18th, 2019, 08:17 AM   #2
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Assume a one-dimensional profile* (velocity is constant at each cross-section).

Treat the water as incompressible, so density $\rho$ is constant.

Conservation of mass:
$\displaystyle \dot{m}=\rho V_1 \left( \frac{\pi D_1^2}{4} \right)=\rho V_2 \left( \frac{\pi D_2^2}{4} \right) = 0.3~L/s$
Find $V_1$ and $V_2$, and plug into Bernoulli's equation.

*Velocity will be zero at the funnel walls. However, if the flow is turbulent and the boundary layer is thin enough, this is a reasonable approximation.
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