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Homework Statement
Problem 16.39
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The viscous force of a liquid in laminar flow through length L is given by ##F_v=4\pi\etaL v_m## where ##\eta## is liquid viscosity and ##v_m## is maximum velocity of the fluid. Find an expression for ##v_m## in terms of p1, p2 (pressure at each end) and in terms of ##\eta , L, r## (r is radius of pipe)
*I'm not solving the whole problem, but I have a question about force.
Homework Equations
##F=p*A##
The Attempt at a Solution
I look at the key and see that they are equating ##F_v## with the pressure difference. Can it just be one pressure?
Is there a difference between representing force as pressure times area as they are (##F=p * A##), versus when one or both of the variables is changing? ( ##F=\Delta p * A## or ##F=p* \Delta A ##). It makes sense to me if both variables are not changing. But if they changes, does it mean the force is changing as well, so we should write the equation as ##\Delta F##?
Thank you!
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