Total Head Loss
There will be both major and minor head loss in this system. The major head loss will come from the friction caused by the water running through the pipe. The minor head loss comes from the opening of the pipe in to the rapid mix basin.
We must first assume a pipe size of 1.5ft in diameter. This works out to 1.767ft2
Velocity Calculation:
Q = V/A
Q = flow rate in ft3/sec = 18.57 ft3/sec
V = velocity of water
A = area of the pipe = 1.767ft2
V = Q/A = 18.57/1.767 = 10.51 ft/s
Now we must find out if the flow is turbulent or laminar. This will decide which method we use to calculate head loss. We use the Reynolds number to define the flow.
Re = ρ*V*D/μ
ρ = density of water = 1 slug/ ft3
V = velocity of water = 10.51 ft/s
D = diameter of pipe = 1.5 ft
μ = kinematic viscosity of water = 0.0000232
Re = 679526
This high Reynolds number means the flow is turbulent.
The major head loss equation is as follows:
hL = (f*L*V2)/(2Dg)
f = friction factor
L = length of pipe
V = velocity of water = 10.51 ft/s
D = diameter of pipe = 1.5 ft
g = gravitation constant (32.2 ft/s2)
To get the friction factor, f, we must make an assumption about the material of our pipe. For this lab, we will assume a concrete pipe. By using the diameter and material of our pipe, we can use Table ?? to find the appropriate friction factor.
hL =
The minor head loss equation is as follows:
hL = 9*KL*V2/2*g
KL = exit loss coefficient
V = velocity of water = 10.51 ft/2
g = gravitation constant (32.2 ft/s2)
To find the exit loss coefficient, we must make an assumption about the way the water will exit the pipe and enter the basin. We will assume that there will be slightly rounded edges at the opening to the basin. This will give us a smaller coefficient value of 1 and reduce the head loss from turbulence. We also must be sure to multiply our minor head loss value by 9 because we have nine basins.
hL = 15.4 ft
Water must also enter each pipe from the basin 9 times. The exit loss coefficient for water entering a pipe with rounded edges is 0.2. The equation is the same for water exiting a pipe.
hL = 3.1 ft
Total hL = hL Major + hL Minor Exit + hL Minor Entry