Consider a constant diameter tube with a u-tube mercury (SG = 13.6) manometer co

Question

Consider a constant diameter tube with a u-tube mercury (SG = 13.6) manometer connected to it as shown.

Consider a constant diameter tube with a u-tube mercury (SG = 13.6) manometer connected to it as shown. Water is flowing downwards. The pressure at point 2 is different than the pressure at point 1 and the u-tube mercury (SG = 13.6) manometer is used to determine the difference P2 - P1. Are you able to use the Bernoulli equation to determine the pressure difference P2 - P1: for this flow? Explain your answer to part a? Speculate on why not the Bernoulli equation is not valid for this problem.

Explanation / Answer

a)

No

b)

P1 + 1/2*rho*V1^2 + rho*g*h1 = P2 + 1/2*rho*V2^2 + rho*g*h2

Since dia is constant, A1*V1 = A2*V2 gives V1 = V2.

Thus, P2 - P1 = rho*g*(h2 - h1)

h2 - h1 = 5*cos45 ft

P2 - P1 = 5*cos45 ft of water

P2 - P1 = 5*cos45 / 13.6 ft of mercury

P2 - P1 = 0.26 ft of Hg = 3.12 in of mercury

This value is less than 6 in of mercury which is measured.

c)

This is because Bernoulli eqn didnot take into account for fricttion in pipe.

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