Pump head calculations are essential for the PE Civil and Mechanical exams. In this tutorial, you'll learn how to build a comprehensive Total Dynamic Head (TDH) calculator in Excel that you can use for exam preparation and professional work.

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Understanding Total Dynamic Head (TDH)

Total Dynamic Head is the total equivalent height a pump must move water. It's the sum of several components:

Total Dynamic Head Equation

TDH = Static Head + Friction Head + Minor Losses + Pressure Head

TDH = (z_d - z_s) + h_f + h_m + (P_d - P_s)/(γ)

Where:

Static Head = Elevation difference between discharge and suction (ft)
Friction Head (h_f) = Energy lost due to pipe friction (ft)
Minor Losses (h_m) = Energy lost through fittings, valves, etc. (ft)
Pressure Head = Difference in pressure requirements (ft)

Excel Spreadsheet Layout

Here's how to organize your spreadsheet:

Cell	Description	Example Value
B2	Flow rate (gpm)	500
B3	Pipe diameter (inches)	6
B4	Pipe length (ft)	1000
B5	Hazen-Williams C	130
B6	Suction elevation (ft)	0
B7	Discharge elevation (ft)	50
B8	Number of 90° elbows	4
B9	Number of gate valves	2

Step-by-Step Formulas

Step 1: Calculate Velocity

First, convert flow rate to velocity:

Excel Formula (Cell B12)

=B2/(449*PI()*(B3/24)^2)

This gives velocity in ft/s. The 449 converts gpm to cfs, and B3/24 converts diameter to feet (radius).

Step 2: Calculate Static Head

Simple difference between elevations:

Excel Formula (Cell B13)

=B7-B6

Result: Static Head in feet

Step 3: Calculate Friction Head Loss

Using Hazen-Williams equation:

Excel Formula (Cell B14)

=10.67*B4*(B2/448.83)^1.852/(B5^1.852*(B3/12)^4.87)

This is the Hazen-Williams equation in one formula. Result in feet.

Step 4: Calculate Minor Losses

Sum of K-values times velocity head:

K-Values for Common Fittings

90° elbow (standard): K = 0.9
45° elbow: K = 0.4
Gate valve (open): K = 0.2
Check valve: K = 2.5
Entrance (sharp): K = 0.5
Exit: K = 1.0

Excel Formula (Cell B15)

=(B8*0.9+B9*0.2+0.5+1.0)*B12^2/(2*32.2)

Includes 4 elbows, 2 gate valves, entrance, and exit losses.

Step 5: Calculate Total Dynamic Head

Excel Formula (Cell B16)

=B13+B14+B15

Sum of static head, friction losses, and minor losses.

Calculate Pump Power

Once you have TDH, calculate the required pump power:

Pump Power Equations

Hydraulic Horsepower: WHP = (Q × TDH × γ) / 550

For water: WHP = (Q × TDH) / 3960

Brake Horsepower: BHP = WHP / η

Excel Formula for Pump HP (Cell B18)

=B2*B16/3960

This gives Water Horsepower. Divide by pump efficiency (e.g., 0.75) for Brake HP.

PE Exam Tip: Remember the magic number 3960! It converts gpm × feet to horsepower for water. For other fluids, use the specific gravity: HP = (gpm × TDH × SG) / 3960

Complete Working Example

Problem: Size a pump for a water system with:

Flow: 500 gpm
6-inch Schedule 40 pipe, 1000 ft long (C = 130)
Lift from ground level to 50 ft tank
4 elbows, 2 gate valves, entrance and exit

Solution:

Velocity = 500 / (449 × π × 0.25²) = 5.67 ft/s
Static Head = 50 - 0 = 50 ft
Friction Loss = 10.67 × 1000 × (500/449)^1.852 / (130^1.852 × 0.5^4.87) = 21.4 ft
Minor Losses = (4×0.9 + 2×0.2 + 0.5 + 1.0) × 5.67² / 64.4 = 2.8 ft
TDH = 50 + 21.4 + 2.8 = 74.2 ft
WHP = 500 × 74.2 / 3960 = 9.4 HP
BHP (at 75% eff) = 9.4 / 0.75 = 12.5 HP → Select 15 HP motor

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