determine the pressure at point(1) if (a) all losses are neglected, (b) the only losses included are skin friction losses, (c) all losses are included
1.5 Pipe Flow Systems
• In the previous sections, we discussed concepts concerning the energy balance and the flow in pipes.
• The purposes of this section is to apply these ideas to the solutions of pipe systems.
Re
1.12 103
45000
Thus ,the flow is turbulent flow
Governing equation for either case (a), (b), or (c) is the mechanical balance equation given by
p1
V12 2
Solution: Since the velocity in the pipe is given by
V1
Q A1
0.756 103
0.01912
2.64m / s
4
And the fluid properties are ρ=999.9kg/m3 and μ=1.12×10-3Pas
999.9 2.64 0.0191
1.5.1 Single Pipes
For flowing through a pipe three most common types of problems are shown in table in terms of the parameters involved.
Variable
type I type II type III
z1g
p2
V22 2
z2g hf
Where z1=0, z2=6.1m, p2=0, and outlet velocity is
V2
Q A2
0.756 103
0.01272z2 g
V22
V12 2
h f
1
Where the friction loss is different for each of three cases
With thisε/D and Reynolds number (Re=45000), the value of friction coefficient is obtained from Moody chart as λ=0.0215.
the potential and kinetic energy are the same as part (a). Eq.1 gives
p1
z2 g
V22
V12 2
L D
V12 2
74133 999.9 0.0215 18.29 2.642 0.0191 2
145872Pa
Of this pressure drop, the amount due to skin friction is 71739 Pa
a. Fluid
Density Viscosity
b. Pipe
Diameter Length Roughness
c. Flow
Flowrate
d. Pressure
Pressure drop
given given given given
given determine
given given given given
due to the increase in kinetic energy
(b)
If only losses included are the skin friction losses , the friction loss is
hf
L V12 D2
Relative roughness ε/D=8×10-5
determine given
given given determine given
given given
Example 1
Water at 15.6ºC flows from the basement to the second floor through the 1.91cm diameter copper pipe (ε = 0.001524mm ) at a rate of Q=0.756 l/s and exits through a faucet of diameter 1.27cm. As shown in Fig.
• We will concern two classes of pipe systems: those containing a single pipe and those containing multiple pipes in parallel, series.
Pipe system
Some of the basic components of a typical pipe system shown in Fig.
(a) If all losses are neglected, Eq.1 gives
p1
6.1 999.9 9.81 999.9 5.972
2.642 2
74133Pa
Note that for this pressure difference, the
amount due to elevation change and amount
They include : • the pipes themselves, • the various fittings used to connect the
individual pipes to form the desired system, • metering devices, and • the pumps or turbines that add energy to or remove energy from the fluid.