Question

When 0.3 m3 /s of water flows through a 150-mm-diameter constriction (B) in a 300-mm-diameter vertical pipeline (A), the pressure at point A in the pipe is 345 kPa, and the head loss between this point (A) and the constriction (B) is 2 m. The pressure in the constriction (B) is 180.3 kPa. How high is the constriction (B) from the point A?

Answer 1

The constriction is 13.94 m high from point A

Explanation:

When we apply energy relation between point A and point B, we get:

Pb/ρg + Vb²/2g= Pa/ρg + Va²/2g - Head Loss - h

where,

Pb = Pressure at constriction (B) = 180.3 KPa = 180300 Pa

Vb = Velocity at constriction (B) = (0.3 m³/s)/π(0.15 m)² = 4.24 m/s

Pa = Pressure at (A) = 345 KPa = 345000 Pa

Va = Velocity at (A) = (0.3 m³/s)/π(0.3 m)² = 1.06 m/s

g = 9.8 m/s²

ρ = density of water = 1000 kg/m³

Head Loss = 2 m

h = Height of constriction = ?

Therefore:

h = (Pa- Pb)/ρg + (Va² - Vb²)/2g - Head Loss

h = (345000 Pa - 180300 Pa)/(1000 kg/m³)(9.8 m/s²) + [(1.06m/s)² - (4.24 m/s)²]/2(9.8 m/s²) - 2 m

h = 16.8 m - 0.86 m - 2 m

h = 13.94 m