In this article (and video above), we calculate the flow rate of water at room temperature through 2,000 ft. of 8-in (8.18-in ID) 20 year old cast iron pipe. This question forms part of the Structural Mechanics section of the PE Exam and was created and solved by Engineer in training, Enrique Ivers, LEED Green Associate.

**Question:**

Water at room temperature flows through 2,000 ft. of 8-in (8.18-in ID) 20 year old cast iron pipe.. The pressure in the pipe drops from 90 psi at the source to 85 psi at the end What is the flow rate in the pipe, in gallons per minute?

**Explanation:**

We should first identify our key information:

- Length of pipe = 2,000 ft
- Internal diameter of the pipe – 8.18 in = 0.68 ft
- Pipe Material – 20 year old Cast Iron (necessary to calculate the Hazen-Williams coefficient!)
- Initial Pressure and Final Pressure – 90 psi and 85 psi respectively, resulting in a difference of 5psi
- Water Temperature – Room Temperature (we can use the Hazen-Williams Equation)
- Unknown Target: Flow rate in the pipe in gpm

We have some key equations at our disposal:

**Flow velocity equation: **

where *v* is flow velocity, *Q* is the volume of flow, and *A* is the cross-sectional area of the pipe.

**Hazen-Williams Equation:**

[Given in the PE Handbook]

*v* is flow velocity, k_1 is 0.849 for SI units and 1.318 for USCS units, *C* is the Hazen-Williams Roughness Coefficient, R_His the hydraulic radius, and *S *is the slope of the energy grade line.

**Circular Pipe Head Loss (as pressure):**

[Given in the PE Handbook as a variation of the Hazen-Williams Equation] where P is the pressure loss (psi per foot of pipe), Q is flow (gpm), D is Pipe Diameter (inches) and C is the Hazen-Williams Coefficient.

In this problem, it’s critical to identify that the water temperature is room temperature.

Identifying this quality allows us to use the Hazen-Williams equation, which is valid only for water between the temperatures of 40°F and 75°F. Otherwise, we would have to use the Darcy-Weisbach equation.

In this problem, it’s critical to identify that the water temperature is room temperature.

Identifying this quality allows us to use the Hazen-Williams equation, which is valid only for water between the temperatures of 40°F and 75°F. Otherwise, we would have to use the Darcy-Weisbach equation.

We meet the conditions and know all of the variables to use the Hazen-Williams Equation for Circular Pipe Head Loss as pressure:

**Answer:**

The correct answer is B.

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I hope you found this article helpful. In upcoming articles, I will solve some more PE exam practice problems and answer other questions from our subscribers. Pass the PE Exam videos will publish weekly, so be sure to click the subscribe button so you don’t miss something that could make a substantial difference in your exam result.

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I’ll see you next week… on Pass the PE Exam

Anthony Fasano, P.E.

Engineering Management Institute

Author of Engineer Your Own Success

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