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Document Preview: Q1Given Data :A 3 km pipe starts from point A end at point B Population = 3000 people Q = 300 L/day/personRoughness = cast ion pipeLength of the pipe = 3kmCase 1 From A to B slope is 0°Case 2 From A to B slope is 5° up ward Case 3 From A to B slope is 3° down ward PlotHead loss20 cm40 cm 80 cm 100 cm 150 cm 200 cm Determine the Head loss ?

Robert · Accepted Answer

Q1 
 
Given Data : 
 
A 3 km pipe starts from point A end at point B  
 
Population = 3000 people  
Q = 300 L/day/person 
Roughness = cast ion pipe 
Length of the pipe = 3km 
 
 
Case 1  
From A to B slope is 0° 
 
Case 2  
From A to B slope is 5° up ward  
 
Case 3  
From A to B slope is 3° down ward  
 
Plot Head loss 
20 cm  
40 cm   
80 cm   
100 cm   
150 cm   
200 cm   
 
 
Determine the Head loss? 
 
 
Solution : 
 
For 20 cm diameter 
Case 1: 
 
Discharge Q=3000 X 300 X10-3 m3/24x60x60 =0.0104 m3/s 
                      
 
                     Diameter D=20 cm =0.2 m 
                     Area of cross section A=0.0314m2 
                    Velocity v=Q/A=0.33 m/s 
      
                   Length =   L=3000 m 
For this pipe apply Bernoulli’s equation at A and B 
 
2 2
2 2
A A B B
A b L
p v P v
Z Z h
w g w g
       
Here  velocities (diameter constant) and elevation is same. 
 
Head loss = 
2
2
A B A
L
p P fLv
H h
w w gD
     
 
For cast iron  roughness ϵ = 0.26 mm 
Relative pipe roughness = ϵ/D=0.26/200=0.0013 
Reynolds number 
2 2(0.045)(3000)(0.33)
3.74
2 2 9.81 0.2
A
L
fLv
H h m of water
gD
   
   
4
(1000)(0.33)(0.2)
74157
8.90 10
e
VD
R

 
  

 
 
From moody chart  f=0.045 
Head Loss
2 2(0.045)(3000)(0.33)
3.75
2 2 9.81 0.2
A
L
fLv
H h m of water
gD
   
 
 
 
Case2: 
 
Here slope = 50 up  
So rise from A to B is 3000 tan 5 =262.4 m 
 
( )B A LH Z Z h   =262.4+3.75=266.1  m 
 
Case 3 
 
Slope 30 Down 
 
So fall from A to B =3000 tan 3=157 m 
 
 Here head will increase due to fall H= 157-hL =157-3.57=153.43 m 
 
 
For 40 cm 
                        
 
Case 1: 
 
Discharge Q=3000 X 300 X10-3 m3/24x60x60 =0.0104 m3/s 
                      
 
                     Diameter D=40 cm =0.4 m 
                     Area of cross section A=0.1256m2 
                    Velocity v=Q/A=0.082 m/s 
      
                   Length =   L=3000 m 
For this pipe apply Bernoulli’s equation at A and B 
 
2 2
2 2
A A B B
A b L
p v P v
Z Z h
w g w g
       
Here  velocities (diameter constant) and elevation is same.

Q1 Given Data : A 3 km pipe starts from point A end at point B Population = 3000 people Q = 300 L/day/person Roughness = cast ion pipe Length of the pipe = 3km Case 1 From A to B slope is 0° Case 2...

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