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 = |h_A – h_B| for the manometer in Fig. P4.1(a).

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

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

Transcribed Image Text:

P P₁ P₂ hc B 10 A Pm C NA h₂ NA P₁ A hc P B P₂ Po ? hB (a) (b) Figure P4.1 Liquid-filled pipes with manometers: (a) manometer liquid denser than that in the pipe (Pm>p) and (2) manometer liquid less dense (p < P).