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iloveannaw
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Homework Statement
A power station has a huge tank to store water. The tank is filled by a pump which is attached horizontally to the bottom edge (the bottom of one of the walls) of the tank. In the floor of the tank is an outflow valve. The valve is subject to huge forces and after some years starts to leak.
Calculate the maximum possible height to which the tank can be filled.
Homework Equations
Static pressure and Newton's Laws
The Attempt at a Solution
This is the first part of a large question. I think this must be a force question, so here goes.
The water pressure consists of static pressure + pressure applied by pump = P = [tex]\rho gh + P_{PUMP}[/tex]
The water pressure exerts a force on the bottom of the tank (and valve) = FBASE = AP = [tex]A \left( \rho gh + P_{PUMP} \right)[/tex]
In turn the valve exerts a reaction force = FVALVE , which is less than the force due to pressure:
FVALVE < FBASE
FVALVE < [tex]A \left( \rho gh + P_{PUMP} \right)[/tex]
[tex]h > \frac{F_{VALVE}-AP_{PUMP}}{A \rho g}[/tex]
Unforutnately the LHS side is not smaller than the RHS. Also having FVALVE and PPUMP in the final equation is also unsatisfactory. I really don't know where to start with this question.
thanks
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