A non-uniform part of a pipe line 5 m long is laid at a slope of 2 in 5. Two pressure gauges each fitted at upper and lower ends read 20 N/cm2 and 12.5 N/ cm2. If the diameters at the upper end and lower end are 15 cm 10 cm respectively. Determine the quantity of water flowing per second.

 

A non-uniform part of a pipe line 5 m long is laid at a slope of 2 in 5. Two pressure gauges each fitted at upper and lower ends read 20 N/cm2 and 12.5 N/ cm2. If the diameters at the upper end and lower end are 15 cm 10 cm respectively. Determine the quantity of water flowing per second.

 

Solution:

 L= 5 m, D1=15cm =0.15m

A₁=π/4 x D1 2 = 0.01767 m2

P₁ =20 N/ cm2 =20x104 N/m2 ,

P₂=12.5N/ cm2 =12.5x104 N/m2  

Dia. At the lower end, D₂=300mm =0.3m

A₂=π/4 x D₂ ² = 0.00785 m2

 Let the datum line is passing through the centre of the lower end

Then z2=0

 

 As slope is 2 in 5 hence, z1=2/5 x5= 2 m

 Q= A₁

V₁=A₂V₂

V₁ = A₂V₂/A₁ =0.00785x V₂ /0.01767 V₁ = 0.444 V2

 Applying Bernoulli’s eqn. at (1) and (2), we get

P₁/ ρg + V₁ ² / 2g +z1 = P2/ ρg + V₂ ² / 2g +z2

7.645 + 2 = V₂ ² /2g x 0.8028

V₂=15.35 m/s

Discharge, Q= A₂V₂ = 0.00785 x 15.35 = 0.1205 m3 /s

Q = 120.5 lit/s