# Fluid Mechanics Calculations and Example Problems in Civil Engineering

## Pipe Flow Calculations

Liquids and gases are transported through pipes for a wide variety of applications. Engineers need to be able to calculate i) the pipe size needed for a given flow rate and available pump head, ii) the head loss due to a given flow rate through a pipe of known size, or iii) the the flow rate through a specified pipe with a given head loss. These articles present the calculation procedure and the equations to be used for each of these types of calculations, as well as example calculations. There are articles on the use of Darcy-Wiesbach/friction factor calculations and on the use of the Hazen Williams formula. Information is also presented on the use of Excel spreadsheets for pipe flow calculations.

- Pipe Flow Calculations 1 - The Entrance Length for Fully Developed Flow
- Pipe Flow Calculations 2 - Reynolds Number for Determining Laminar or Turbulent Flow
- Pipe Flow Calculations 3 - The Friction Factor and Frictional Head Loss
- Pipe Flow/Head Loss/Friction Factor Calculations with Excel Spreadsheets
- Excel Formulas to Calculate Water Flow Rates for Different Pipe Sizes

## Uniform Open Channel Flow Calculations

For open channel flow, a free liquid surface is open to atmospheric pressure, so the driving force for flow is gravity, rather than a pressure difference as in pipe flow. Examples of open channel flow include flow in rivers and streams, in storm sewers, in arroyos and irrigation channels, and in man-made open channels such as those used in wastewater treatment plants. Uniform open channel flow occurs when a constant flow rate passes through a channel with constant bottom slope, constant surface roughness, and constant shape and size. These articles center on the use of the Manning equation for uniform open channel flow, including calculation of the hydraulic radius, determination of the flow rate in a given channel at a given depth of flow and determination of the normal depth of flow, for a given channel and flow rate. There are articles on natural channel calculations and articles that emphasize calculations for man-made channels.

- Introduction to the Manning Equation for Uniform Open Channel Flow Calculations
- Calculation of Hydraulic Radius for Uniform Open Channel Flow
- Calculation of Normal Depth for Open Channel Flow
- Calculating Uniform Open Channel Flow/Manning Equation Solutions with Excel Spreadsheets
- Use of the Manning Equation for Open Channel Flow in Natural Channels
- Determining the Manning Roughness Coefficient for a Natural Channel
- Manning Equation Calculations for Partially Full Pipe Flow
- How to Use the Manning Equation for Storm Sewer Calculations

## Open Channel Flow Measurement

Weirs and flumes are the most common devices for measuring flow rate in open channels. These articles include information about sharp crested, rectangular and V-notch weirs, broad crested weirs, and Parshall flumes. The information includes descriptive material, diagrams, equations, example calculations, and discussion of the use of Excel spreadsheets for the calculations.

- Open Channel Flow Measurement 1: Introduction to the Weir and Flume
- Open Channel Flow Measurement with V-Notch Weirs
- Open Channel Flow Measurement with Rectangular, Sharp-Crested Weirs
- Open Channel Flow Measurement with Parshall Flumes
- Open Channel Flow Measurement with Broad Crested Weirs
- Excel Spreadsheets for V-Notch Weir Flow Measurement Calculations
- Excel Spreadsheets for Rectangular Weir Flow Measurement Calculations
- Excel Spreadsheets for Parshall Flume Flow Measurement Calculations
- Excel Spreadsheets for Broad Crested Weir Flow Measurement Calculations

## Pipe Flow Measurement

A widely used type of flow measurement device for pipe flow is the differential flow meter, including flow nozzle, orifice, and venturi meters. These meters use a constriction in the flow area to increase the fluid velocity and thus decrease the fluid pressure. The amount of pressure decrease can then be measured and used to calculate the flow rate. Descriptive material, equations, and example calculations are included for flow nozzle, orifice, as well as venturi meters, along with information about pitot tubes, rotameters, and magnetic flow meters.

- The Orifice, Flow Nozzle, and Venturi Meter for Pipe Flow Measurement
- Use ISO 5167 to Find the Orifice Discharge Coefficient for an Orifice Flow Meter
- Excel Templates for Venturi and Orifice Flow Meter Calculations
- How to Measure Fluid Velocity with a Pitot Tube
- Measurement of Pipe Flow Rate with a Rotameter Flow Meter
- Pipe Flow Measurement with a Magnetic Flow Meter

## Hydraulic Jumps and Supercritical Open Channel Flow

Hydraulic jumps occur in order to make a transition from supercritical flow to subcritical flow on a channel that isn’t steep enough to maintain supercritical flow. The articles in this section provide background information about subcritical, critical, and supercritical flow, about hydraulic jump calculations, and about calculation of parameters like critical depth and critical slope for open channel flow.

- Subcritical, Critical and Supercritical Open Channel Flow
- Open Channel Flow Basics - Hydraulic Jump Calculations
- Use of Excel Formulas for Hydraulic Jump Calculations
- Calculation of Critical Depth and Critical Slope for Open Channel Flow

## Fluid Mechanics Fundamentals

Fundamental fluid mechanic principles are useful in a variety of ways. For example, the Ideal Gas Law can be used to calculate the density of air and other gases at different tempertures and pressures. The equations and methods of calculating drag force due to fluid flow past an immersed object can provide insight into the reason why the dimples in golf balls make the golf balls go farther than smooth balls would.

- What is the Ideal Gas Law?
- Drag Force for Fluid Flow Past an Immersed Object
- How Do Golf Ball Dimples Reduce Air Resistance and Make Balls Go Farther?
- The Continuity Equation and Common Fluid Flow Rate Parameters
- Use the Ideal Gas Law to find the Density of Air at Different Pressures and Temperatures

## References

- International Organization of Standards - Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full. Reference number: ISO 5167-2:2003.
- Munson, B. R., Young, D. F., & Okiishi, T. H., Fundamentals of Fluid Mechanics, 4th Ed., New York: John Wiley and Sons, Inc, 2002.
- U.S. Dept. of the Interior, Bureau of Reclamation, 2001 revised, 1997 third edition,
*Water Measurement Manual.*