Pump Head Calculation: Total Dynamic Head Formula
Learn how to calculate total dynamic head (TDH) for wastewater pumps. Step-by-step formula, worked example, and common exam traps.
What Is Total Dynamic Head and Why Does It Show Up on the Exam?
Total dynamic head (TDH) is the total amount of resistance a pump has to overcome to move water from one point to another. It's the single number that tells you how hard your pump is working, and the pump head calculation is one of the most commonly tested pump-related formulas on wastewater certification exams.
Here's the thing: most operators don't calculate TDH on a daily basis. Your pumps are already sized and installed. But the exam doesn't care about that. Pump head calculation questions can show up on Grade 1 through Grade 4 exams, depending on the state or certifying body, and they trip people up because the concept involves several pieces that you have to add together correctly.
How Do You Calculate Total Dynamic Head?
TDH is the sum of static head, friction head, and velocity head. This covers the common scenario where both the suction and discharge sides are open to atmosphere. If the system involves pressurized conditions (such as back pressure on a force main), a pressure head term must also be included.
In most exam problems, velocity head is negligible and gets ignored, so the TDH formula you'll use most often is:
TDH (ft) = Static Head (ft) + Friction Head (ft)
When the exam gives you velocity head or pressure head, the full version looks like this:
TDH (ft) = Static Head + Friction Head + Velocity Head (+ Pressure Head if applicable)
Let's break down each piece so you know exactly what you're adding up.
What Is Static Head?
Static head is the vertical distance the water has to travel. In most exam problems with open tanks on both ends, it's the elevation difference between the suction water surface and the discharge point, measured in feet.
If you're pumping from a wet well that's 12 feet below ground up to a discharge point that's 8 feet above ground, your static head is 20 feet. You're just measuring the vertical lift from the water surface at the suction side to the water surface (or discharge point) at the delivery side.
The simplest and most reliable way to calculate total static head is:
Total Static Head = Discharge Water Surface Elevation - Suction Water Surface Elevation
This formula works regardless of whether the pump is above or below the water level.
On the exam, static head is sometimes broken into two parts:
- Static suction lift: The vertical distance from the water surface up to the pump centerline (water level is below the pump)
- Static suction head: The vertical distance from the water surface down to the pump centerline (water level is above the pump, also called flooded suction)
- Static discharge head: The vertical distance from the pump centerline to the discharge point
If you have a suction lift (water below the pump), you add it to the discharge head to get total static head. If you have a suction head (flooded suction, water above the pump), you subtract it from the discharge head. Using the elevation difference method above avoids confusion with sign conventions entirely.
Exam Tip
Watch for exam questions that give you the elevation of the wet well floor instead of the water surface. Static head is measured from the water surface, not the bottom of the tank. If the wet well floor is at 90 ft elevation but the water level is at 95 ft, use 95 ft.
What Is Friction Head?
Friction head is the energy lost to friction as water moves through the pipes, fittings, valves, and elbows. Every foot of pipe, every bend, every partially closed valve adds resistance.
In real design work, engineers use tables and software to calculate friction losses based on pipe diameter, length, material, and flow rate (Hazen-Williams equation, Darcy-Weisbach, etc.). On the exam, they almost always just give you the friction loss as a number. You don't have to calculate it from scratch.
A typical exam question looks like: "Friction losses in the system are 4.5 feet." You just plug that number in.
If the exam does ask you to figure out friction loss, they'll provide a friction loss chart or tell you something like "friction loss is 2.5 ft per 100 ft of pipe" and give you the pipe length. That's just multiplication.
What About Velocity Head?
Velocity head accounts for the kinetic energy of the water at the discharge point. It's calculated as:
Velocity Head = v² / (2 × g)
Where v is velocity in ft/s and g is gravity (32.2 ft/s²).
Here's the good news: velocity head is usually small (often less than 1 foot at typical pipe velocities below about 8 ft/s) and most exam questions either ignore it entirely or tell you to disregard it. Unless the problem specifically mentions velocity head or gives you a discharge velocity, don't worry about it.
Worked Example: Calculating TDH
Here's a typical exam-style pump head calculation problem:
Worked Example
Given:
- Wet well water surface elevation: 92 ft
- Discharge point elevation: 115 ft
- Friction losses in the piping system: 6.3 ft
- Velocity head is negligible
Step 1: Calculate static head Static Head = Discharge Elevation - Suction Water Surface Elevation Static Head = 115 ft - 92 ft = 23 ft
Step 2: Add friction head TDH = Static Head + Friction Head TDH = 23 ft + 6.3 ft
Step 3: Solve TDH = 29.3 ft
Answer: TDH = 29.3 ft
That's it. Plug and chug. The math isn't hard. The challenge is knowing which numbers go where.
Worked Example: TDH with Velocity Head
Sometimes the exam throws in velocity head just to test whether you know the full formula:
Worked Example
Given:
- Static suction lift: 10 ft
- Static discharge head: 18 ft
- Friction losses: 5.2 ft
- Discharge velocity: 8 ft/s
Step 1: Calculate total static head Static Head = Suction Lift + Discharge Head Static Head = 10 ft + 18 ft = 28 ft
Step 2: Calculate velocity head Velocity Head = v² / (2 × g) Velocity Head = (8)² / (2 × 32.2) Velocity Head = 64 / 64.4 Velocity Head = 0.99 ft ≈ 1.0 ft
Step 3: Add all components TDH = Static Head + Friction Head + Velocity Head TDH = 28 ft + 5.2 ft + 1.0 ft
Step 4: Solve TDH = 34.2 ft
Answer: TDH = 34.2 ft
See how the velocity head was only about 1 foot? That's typical. It's a small piece of the puzzle, but if the exam asks for it, you need to include it.
How Does TDH Connect to Pump Sizing?
In the plant, TDH is what determines how powerful your pump needs to be. A pump curve plots flow rate against head, and as TDH increases, the flow a pump can deliver decreases. When you match TDH to a pump curve, you find your operating point.
You might see exam questions that tie TDH into water horsepower or brake horsepower calculations. Water horsepower uses TDH directly:
Water HP = (Flow in gpm × TDH in ft) / 3,960
That 3,960 constant is worth memorizing. If the exam gives you a TDH and a flow rate, they might ask you to find the horsepower needed, and that formula connects directly to the TDH you just calculated.
Common Pump Head Calculation Mistakes on the Exam
Confusing static head with total pipe length. Static head is only the vertical distance. If the exam says the pipe runs 200 feet at a slope to cover a 15-foot elevation change, the static head is 15 feet, not 200 feet. The pipe length affects friction losses, not static head.
Forgetting that static head uses water surfaces. If you're pumping from one tank to another, measure from the water surface in the suction tank to the water surface in the discharge tank, not from the pipe inlet to the pipe outlet.
Confusing suction head with suction lift. If the water level is above the pump centerline (flooded suction), that's suction head and it reduces your total static head. If the water level is below the pump centerline, that's suction lift and it increases total static head. Using the elevation difference method (discharge elevation minus suction elevation) avoids this confusion entirely.
Adding pressure head incorrectly. If the discharge is into a pressurized system (like a force main with back pressure), you might need to convert that pressure to feet of head. The conversion is:
- 1 psi = 2.31 ft of head
So 10 psi of back pressure adds 23.1 feet to your TDH.
Using the wrong units for velocity head. Make sure velocity is in ft/s and you're using 32.2 ft/s² for gravity. If you accidentally use meters, your answer will be way off.
Exam Tip
If an exam question gives pipe pressure in psi, convert to feet of head by multiplying by 2.31. This is a common unit conversion trap, and the answer choices will include the wrong answer you'd get if you forgot to convert.
When Would You Use TDH in the Plant?
You probably won't calculate TDH from scratch on your shift. But understanding total dynamic head helps you troubleshoot. If a pump isn't delivering the flow it should, the TDH might have changed. A partially clogged force main increases friction head. A higher water level in the discharge tank increases static head. Both mean your pump is working against more resistance and delivering less flow.
Knowing TDH also matters when you're involved in pump replacement decisions or talking with engineers about upgrades. If your detention time calculations show you need more flow through a basin, you need to know whether your existing pumps can handle the head.
The EPA's NPDES Permit Writers' Manual and similar agency publications reference hydraulic design considerations including TDH in pumping station design. Many state regulatory agencies require hydraulic analysis, including TDH calculations, as part of pump station design review - though specific requirements vary by state and permit type.
Key Takeaway
Total dynamic head (TDH) equals Static Head + Friction Head + Velocity Head (if given) + Pressure Head (if the system is pressurized). Static head is the vertical elevation difference between the suction water surface and the discharge point. Friction head represents pipe and fitting losses - usually given directly on the exam. Velocity head (v² / 2g) is almost always negligible at typical pipe velocities. To convert pressure to head, multiply psi by 2.31. Get the static head right and the rest is just addition.
Quick Reference Summary
| Component | What It Measures | How You Get It on the Exam |
|---|---|---|
| Static Head | Vertical elevation difference (ft) | Subtract suction water surface from discharge elevation |
| Friction Head | Pipe and fitting losses (ft) | Usually given directly in the problem |
| Velocity Head | Kinetic energy at discharge (ft) | v² / (2 × 32.2), often negligible |
| Pressure Head | Back pressure converted to ft | psi × 2.31, if applicable |
| TDH | Total pump resistance (ft) | Add all components together |
| Useful Conversion | Value |
|---|---|
| 1 psi | 2.31 ft of head |
| 1 ft of head | 0.433 psi |
| Gravity (g) | 32.2 ft/s² |
| Water HP constant | 3,960 |
If pump head calculations are giving you trouble, work through a few practice problems until the setup feels automatic. The math is simple addition - it's knowing which numbers to grab from the word problem that makes or breaks your answer. For more on how flow rates tie into treatment unit sizing, check out our guide on hydraulic loading rate calculations.