Pressure Drop due to Friction

Incorporate this Visual Basic for Applications (VBA) function into your Excel spreadsheets to calculate the pressure drop for water flowing in pipes. You must enable macros for your spreadsheet; if you use Excel 2007 or later, open the workbook then save it in the new macro-enabled format (.xlsm). Click here to download the file.

This free download is restricted to liquid water and U.S. units (pounds, inches/feet, deg F). Our PIPESIZE spreadsheet is much more flexible, with VBA functions for both U.S. and SI units and the capability to solve compressible flow pressure drop formulas iteratively (for isothermal or adiabatic gas flow).

The VBA function returns one of three values, given the other two. If you enter the flow rate and upstream pressure, it returns the downstream pressure. Enter the upstream and downstream pressures and it returns the flow rate. For each calculation, the pipe diameter, equivalent length of the pipe, its surface roughness, and the water temperature must be entered.

The function syntax is:

=PDUSa(W, Pin, Pout, d, L, epsilon, Optional Tin)

Where

Specify two of the following three; function computes the third

W = mass flow rate, lb/hr

Pin = inlet, or upstream, pressure, psia

Pout = outlet, or downstream pressure, psia

Pipe properties

d = pipe inside diameter, inches

L = pipe length, equivalent feet

epsilon = Surface roughness is in units feet

Water properties are calculated in the function from the water temperature

Tin -- inlet temperature, deg F (default to 60)

Pressure drop due to friction is required to solve wide variety of problems. For a closed-loop system, the pressure drop from friction defines the energy required to move the fluid through the pipe. If the discharge of the pipe is at a different elevation (height) than the inlet, then the static difference is added to the pressure drop from friction to get the total pressure drop. When the system includes networked piping (where the branches come back together such as in a sprinkler system), pressure drop through the branches is equated. I used this VBA function when creating a water distribution model for a client.

## Equivalent Length of Pipe

In the Equivalent Length method, fittings are assigned a resistance value expressed in terms of length of straight pipe. Or, fittings are assigned a resistance expressed as equivalent length divided by diameter. A long radius elbow in a DN 50 (2 inch) pipe offers the same resistance to flow as about 1 meter (3.4 feet) of straight pipe. Sum the equivalent length of all fittings in the pipe, add to the actual length of the pipe (including distance through fittings) and use the resultant as the Length factor in the equations in the next sections.

For new designs, where fittings have not yet been determined, a rule of thumb is to estimate the total length of the pipe then add 50% to 100% as a factor for fittings.

Find the equivalent length for fittings in reference books, including *Rules of Thumb for Chemical Engineers*.

## Water Properties

For the function described here which is restricted to water, I chose to estimate the properties (viscosity and density) using these two formulas:

Viscosity, lb/ft-h = -0.23535 + 208.65 / T - 2074.8 / T^{2}

Density, lb/ft^{3} = 62.7538 - 0.00353 * T - 0.0000482 * T^{2}

Where T is the water temperature, °F

Source: Dickey, David S., "Practical Formulas Calculate Water Properties," Parts 1 and 2, Chemical Engineering, September and November 1991

Formulas for Pressure Drop due to Friction

The calculation is conducted in three steps. First, the Reynolds number is computed. Then, the Darcy (or Moody) friction factor is calculated. Finally, the pressure drop is calculated. These formulas perform the three steps.

Source: Hall, Stephen, Rules of Thumb for Chemical Engineers, 5th Edition, Elsevier (2012)

The Reynolds number, N_{Re}, is a dimensionless number that relates inertial and viscous forces. It is used in the friction factor correlation, to determine the resistance to flow by a pipe.

*D* = pipe diameter, m or ft

*U* = average fluid velocity, m/s or ft/s =

µ = fluid dynamic viscosity, kg/m-s or lb/ft-h

= density of liquid, kg/m3 or lb/ft3, or gas =

Churchill developed an expression for friction factor that spans all flow regimes (laminar, turbulent, and transitional). It agrees with the original Colebrook-White equation, which requires an iterative or graphical solution, while also obtaining the correct result for Reynolds numbers below 2000 (laminar flow regime). The Darcy friction factor according to Churchill’s equation is:

Source: Churchill, S. W., “Friction Factor Equation Spans all Flow Regimes,” Chemical Engineering, 84:24, p 91, 1977.

This incompressible flow equation for liquids can also be used for gases when the pressure drop is less than 10% of the upstream pressure.

L = pipe equivalent length, m or ft

= conversion factor, 1 m/s2 or 32.17 ft/s2

Notice that the VBA function takes care of the units for the formulas once the inputs are provided in the required units. PIPESIZE adds compressible flow equations that are described in *Rules of Thumb for Chemical Engineers*.

*Recommended surface roughness values for various piping materials. Never use a value less than 0.0000015 m or 0.000005 ft, which are the limiting values that define “smooth” pipe.*

Source: Hall, Stephen, Rules of Thumb for Chemical Engineers, 5th Edition, Elsevier (2012)

Pipe Material |
Surface Roughness, m |
Surface Roughness, ft |

Copper, drawn, tubing |
0.000002 |
0.0000067 |

Glass, drawn tubing |
0.000002 |
0.0000067 |

Plastic, drawn tubing |
0.000002 |
0.0000067 |

Brass, drawn |
0.000002 |
0.0000067 |

Iron, cast – new |
0.0003 |
0.0021 |

Iron, wrought – new |
0.000045 |
0.00017 |

Iron, galvanized |
0.00015 |
0.0005 |

Iron, asphalt coated |
0.00015 |
0.0005 |

Steel, new |
0.000045 |
0.00015 |

Steel, lightly corroded |
0.0003 |
0.00125 |

Steel, heavily corroded |
0.002 |
0.0067 |

Steel, galvanized |
0.00015 |
0.0005 |

Steel, polished (hygienic) |
0.000002 |
0.0000067 |

Steel, stainless, drawn tubing |
0.000002 |
0.0000067 |

Sheet metal ductwork, smooth joints |
0.00003 |
0.0001 |

Concrete, very smooth |
0.00004 |
0.00013 |

Concrete, wood floated, brushed |
0.0003 |
0.001 |

Concrete, rough, visible form marks |
0.002 |
0.0067 |

Rubber, smooth tubing |
0.00001 |
0.000033 |

Rubber, wire reinforced |
0.001 |
0.0033 |