An inverted U-tube manometer is used to measure the pressure difference between two pipes A and B, as shown in the figure. Pipe A is carrying oil(specific gravity=0.8) and pipe B is carrying water. The densities of air and water are 1.16 kg/ $m^{3}$ and 1000 kg/ $m^{3}$ , respectively. The pressure difference between pipes A and B is _____kPa.
Acceleration due to gravity:g = 10 m/ $s^{2}$

-2.199

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Solution

The correct option is A -2.199

Given data:
specific gravity of oil
$S_{o i l}$ =0.8
$∴$ $ρ_{o i l} = 0.8 \times 1000 = 800 k g / m^{3}$
density of air : $ρ_{a i r} = 1.16 k g / m^{3}$
Density of water ,
$ρ_{w} = 1000 k g / m^{3}$
Acceleration due to gravity.
$g = 10 m / s^{2}$
$h_{1} = 80 m m = 0.08 m$
$h_{2} = 200 m m = 0.2 m$
$h_{3} = 100 m m = 0.1 m$
pressure at section 1 on left limb =Pressure at section 1 on right limb
$P_{A} - ρ_{o i l} g h_{2} - ρ_{a i r} g h_{1} = P_{B} - ρ_{w} (h_{1} + h_{2} + h_{3})$
$P_{A} - 800 \times 10 \times 0.2 - 1.16 \times 10 \times 0.08 = P_{B} - 1000 \times 10 (0.08 + 0.2 + 0.1)$
$P_{A} - 1600 - 0.928 = P_{B} - 3800$
or $P_{A} - P_{B} = - 2199.07 P a$
= -2.199 kPa

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