One way to monitor the flow rate in a pipe is to use a manometer to measure the

Question

One way to monitor the flow rate in a pipe is to use a manometer to measure the pressure drop P1-P between taps spaced a known distance apart. Two arrangements for liquid pipe flow are shown in Eig. P4.1. The U-tube is placed below the pipe if the manometer fluid is relatively dense and above it if the manometer fluid is less dense. The distance of point i (A, B, or C) from the nearest pipe wall is h. Flow through the U-tube itself can be made negligible by using a small diameter. P2 Fioure P4.1 Activate Win

Explanation / Answer

a) Starting from point 1, we add pressures as we go down and subtract as we go up. Thus, we have

P1 + ghA = PA

Now in the right sided limb, at the same horizontal point, pressure is this value itself since the fluid is same.

A length of (hA - hB) of fluid with density m lies above, and then above it is the test fluid itself. Thus, we have

P1 + ghA - mg (hA - hB) - ghB = P2

Thus, P1 - P2 = (m- )g(hA - hB) = (m- )gh

b) Theoritically, hA=hB but there occurs frictional pressure loses along the direction of the flow. Hence, pressure at B is marginally lower than that at A. Thus, hA > hB or hB is lesser than hA,

c) Dividing the previously obtained equation by , we get

(P1 - P2)/ = (m - 1)h

Since the LHS are same,

we have hHg/hoil = (m - 1)oil/(m - 1)Hg = (0.8-1)/(13-1) = -0.01667

Or rise using oil is 60 times of that when mercury is used and also in the opposite direction.

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