The two pipes (A and B) contain the same liquid with a density of 923 kg/m3. The differential pressure reading in the manometer is found to be h = 0.3m of mercury (density = 13550 kg/m3). Due to changes in pumping, pressure in pipe A increases by 10kPa. What should be the value of hin the manometer at that time?

hm = 0.37 m

Explanation:

Given:

Density of liquid contain in pipes

ρ = 923 kg/m3

Density of manometric fluid

ρ m = 13550 kg/m3

Pressure in the pipe A,

P = 10K Pa

1 - Find the initial pressure difference in pipes, we can apply hydrostatic force concept in both the pipes

P A + ρAghA - PB - ρBghB - ρmghm = 0

P A - P B = 923 * 9.8 * 0.1 + 13550 * 9.8 * 0.3 - 923 * 9.8 * 0.1

P A - P B = 39690 N

(P A + 1000) + ρAghA - PB - ρBghB - ρmghm

PA - PB + 1000 = ρmghm - ρAghA - ρBghB

PA - PB + 1000 = 13550 * 9.8 * hm + 923 * 9.8 * 0.1 - 923 * 9.8 * 0.1

Now put the value from (1) the manometric height

hm = 0.37 m