EXAMPLE 6.1.10. TOTAL HEAD LOSS

Problem: Water flows from the basement to the second floor through the 2cm diameter copper pipe ( a drawn tubing) at a rate of Q= 0.80 liters per second and exits through a faucet of diameter 1.30 cm. Determine the pressure at point 1 if:

1. Viscous effects are neglected
2. The only losses included are major losses
3. All losses are included

With the given Q=0.80 lt/s

   Pipe diameter  = 2cm

   Viscosity         = 

Determine pressure at station 1.

Solution:

a. Pressure at station 1 when there is no head loss

Energy equation between (1) and (9):



     where: 
                   
                     
                          z1 = 0
                      P9 = 0
                      z9 = 8.12 m





So pressure head is:


 compare with z = 8.12m

b. Pressure at station 1 when there is only major head loss


From the same basic BEE equation, add head loss to station 9. After rearranging, you will get:


 
Using Moody diagram, f can be projected using Re=45062 and 

f = 0.0215
L = total length of pipe from station 1 to station 9 = 4.6m+ 6(3m) = 22.60m








c. Pressure at station 1 including all head losses

With the same BEE equation, add major head loss (using Darcy Weisbach formula) and minor losses (in terms of velocity head), then you get: