Pressure and heights of a manometer -- Find the fluid flow rate

  • #1

Homework Statement


Find the flow rate of water. The fluid in the manometer is mercury. ##d_{1},d_{2}## are the diameters in the figure
35k3bqr.png


Homework Equations


Bernoulli, continuity equations

The Attempt at a Solution



We know that

##p_{1}=p_{1Top}+\rho_{water}gh_{2}##, ##p_{2}=p_{2Top}+\rho_{water}gh_{3}##

which means

##p_{1Top}-p_{2Top}=p_{1}-p_{2}+\rho_{water}gh##

on the other hand

##p_{1}-p_{2}=\rho_{Hg}gh##

so

##p_{1Top}-p_{2Top}=gh(\rho_{water}+\rho_{Hg})##

But in the solution it is

##p_{1Top}-p_{2Top}=gh\rho_{Hg}##

where did I go wrong?
 

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Answers and Replies

  • #2
TSny
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We know that

##p_{1}=p_{1Top}+\rho_{water}gh_{2}##, ##p_{2}=p_{2Top}+\rho_{water}gh_{3}##

which means

##p_{1Top}-p_{2Top}=p_{1}-p_{2}+\rho_{water}gh##
Check the sign of the last term on the right side of the second equation. This will modify your result.
Otherwise, I don't see anything wrong with your work. It does appear that the solution you were given is incorrect.
 
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