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A U-tube manometer containing a liquid of specific gravity S measures gauge pressure of water flowing in a pipe. h2 = difference in level of manometric liquid in the two limbs h1 = height of water between point of connection of pressure tap and level of manometric liquid in the limb to which it is connected by a tube bending down. The measured gauge pressure is:

A U-tube manometer containing a liquid of specific gravity S measures gauge pressure of water flowing in a pipe. h2 = difference in level of manometric liquid in the two limbs h1 = height of water between point of connection of pressure tap and level of manometric liquid in the limb to which it is connected by a tube bending down. The measured gauge pressure is: Correct Answer (h<sub>2</sub>.S – h<sub>1</sub>) m of water

Concept:

Let PA be the pressure in the pipe and P0 be the atmospheric pressure.

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ρm = Density of mercury, ρw = Density of water

S = Specific gravity = ρm / ρw ⇒ ρm = Sρw

Balancing the pressure about datum (dotted line is the datum),

PA + ρwgh1 = P0 + ρmgh2

PA – P0 = ρmgh2 - ρwgh1

ΔP (Gauge pressure) = g (ρmh2. –  ρwh­1),

ΔP = gρw (Sh2 - h1)   

ΔP/(ρwg) = (h2.S – h­1) m of water

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