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

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One way to monitor the flow rate in a pipe is to use a manometer to measure the pressure drop P1 – P2 between taps spaced a known distance apart. Two arrangements for liquid pipe flow are shown in Fig. 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 hi. Flow through the U-tube itself can be made negligible by using a small diameter.

(a) Relate P1 − P2 to h = |hA – hB| for the manometer in Fig. P4.1(a).

(b) For the manometer in Fig. P4.1(b), will hB be greater than or less than hA? Again relate P1 − P2 to h.

(c) If the same pressure drop for water is measured by manometers containing mercury (ρm/ρ = 13) or an oil (ρo/ρ = 0.80), how will the values of h compare?

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