A U-tube manometer is placed between two tanks A and B as sketched. The fluid in

Question

A U-tube manometer is placed between two tanks A and B as sketched. The fluid in tank A (and on the left side of the manometer) has density rho A, which is in general different from density rho B (in tank B and on the right side of the manometer). The manometer fluid density is rho m. which is larger than both rho A and rho B. Generate an expression for pressure rho A in terms of the other variables (the densities. rho B, and the given elevations). Simplify your expression for the case where rho A = rho B = rho. Further simplify your expression for the case where rho

Explanation / Answer

a) equationg pressure for sides at height h1

Pa + ag(Za - Z1) = Pb + bg(Zb - Z2) + mg(Z2 - Z1)

Pa = Pb + bg(Zb - Z2) + mg(Z2 - Z1) - ag(Za - Z1)

b) Pa = Pb + g(Zb - Z2 - Za + Z1) + mg(Z2 - Z1)

Pa = Pb + g[(Zb - Za) - (Z2 - Z1)] + mg(Z2 - Z1)

Pa = Pb + (Z1 - Z1)[mg - g] + g[Zb - Za]

c) now when << m

Pa = Pb + (Z1 - Z1)[mg - g] + g[Zb - Za]

Pa = Pb + mg(Z1 - Z1) + g[Zb - Za]

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