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Resolving forces and the resultant mass flows in the "x" direction,
$\sum{P_x A_x} = \sum{\dot{m}V_x}$.
So $P_{in}A_{in} - P_{out}A_{out} = \rho A_{in}V_{in}(V_{out} -
V_{in})$.
$\therefore P_{out}A_{out} = P_{in}A_{in} - \rho
A_{in}V_{in}(V_{out} - V_{in})$.
but $A_{out}V_{out} = A_{in}V_{in}$ (conserve mass), so
$P_{out}A_{out} = P_{in}A_{in} - \rho A_{in}V_{in}^2(A_{in}/A_{out}
- 1)$.
But, $\dot{m} = \rho A_{in}V_{in} \therefore V_{in} = \dot{m}/\rho
A_{in}$
$\therefore P_{out} = (P_{in}A_{in} - \rho
A_{in}(\dot{m}/\rho/A_{in})^2)(A_{in}/A_{out} - 1)/A_{out}$
$= (P_{in}A_{in} - (\dot{m})^2/\rho/A_{in})(A_{in}/A_{out} -
1)/A_{out}$
Entering the data we have, $P_{out} = 1999975Pa$.
There might be a structural problem with the tank because of the
offset distance between the pipes, such that the pressure force in
the pipes would generate a twisting moment. This was a problem in
the Flixborough disaster.