Verify that the flow is turbulent.
The mechanical-energy balance provides a basis for estimating pressure drop owing to friction in fluid flow. For steady flow of an incompressible fluid in a horizontal pipe of constant cross-sectional area, it may be written,
where 
is the Fanning friction factor. Churchill gives the following expression for 
for turbulent flow:
Here, Re is the Reynolds number and ? /D is the dimensionless pipe roughness. For pipe flow, Re ? u?D/?, where D is pipe diameter and ? is dynamic viscosity. The flow is turbulent for Re > 3000.
Consider the flow of liquid water at 25°C. For one of the sets of conditions given below, determine 
and 
Assume ? /D = 0.0001. For liquid water at 25°C, ? = 
, and ? =
(a) D = 2 cm, u = 1
(b) D = 5 cm, u = 1
(c) D = 2 cm, u = 5 
(d) D = 5 cm, u = 5
a. First, the Reynolds number must be determined:
Next, using the equation for the fanning friction factor given, we get
With the friction factor, the ? and ?P ?L can be determined:
b. Re = 
c. Re = 
d. Re = 
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