Question

A manometer containing mercury is connected to two points A and B 15 m apart, on an inclined pipeline conveying water as shown.?

The pipeline is straight and slopes at an angle of 15 o with the horizontal. The manometer gives a reading of 150 mm. Calculate the pressure difference between the two points A and B. (Specific weight of water = 9.81 kN and S.G of Hg= 13.6)

Answer 1

If pressure at point `A` is `P` and at `B` is `P'`,then considering pressure at a horizontal level passing through `s` we can write,

`P+(pq+qr+rs) rho*g=P' + qr*rho* g + rs *13.6*1000*g` (`1 g/(cm^3) = 1000 (Kg)/m^3`)

where, `rho*g=9.8kN`

Now,from the diagram `pq=15 sin 15=3.87m`

given, `rs=150/1000 m`

So,putting the values we get,

`P + 3.87*rho*g +qr*rho*g +rs*rho*g = P' +qr*rho*g +19992`

or,`P +3.87*9.8*10^3 +(150/1000)*9.8*10^3=P'+19992`

or, `P-P'=19992-39396=-19404 Pa`