Pump Discharge Pressure Formula: How to Calculate PDP Step by Step

Pump discharge pressure, or PDP, is the pressure a pump operator sets at the panel so that the nozzle at the end of the hose gets the pressure it was designed for. The formula is short:

Nozzle pressure, plus friction loss, plus elevation pressure, plus appliance loss. If you can fill in those four numbers for the line in front of you, you can set the pump correctly. This article explains where each number comes from, works four examples in both psi and kPa, and covers what changes when you are pumping more than one line.

What pump discharge pressure actually is

The pressure gauge on a nozzle and the pressure gauge on the pump panel never agree, and they should not. Water loses pressure as it rubs along the hose lining, loses more every time it climbs a floor, and loses a chunk every time it passes through a wye, a standpipe, or a master stream device. The pump has to supply all of those losses on top of the pressure the nozzle needs to do its job.

That is why the operator cannot simply "pump 100 psi" to a fog nozzle rated for 100 psi. By the time the water reaches the nozzle, most of that pressure has been spent in the hose, and the stream is weak, short, and poorly formed. PDP is the number that makes the nozzle see the pressure it was built for, after every loss between the panel and the tip.

IFSTA writes the same relationship as PDP = NP + TPL, where total pressure loss (TPL) bundles friction loss, elevation, and appliances. The expanded version is easier to work with, because each term has its own rule.

The four terms of the formula

Nozzle pressure (NP)

Nozzle pressure is the easy one. It is set by the nozzle design and you look it up rather than calculate it.

Some automatic and low-pressure fog nozzles run at 50 or 75 psi. Always use the pressure stamped on the nozzle or in the manufacturer's data. On an exam, the question will tell you the nozzle type and you supply the pressure from this table.

Friction loss (FL)

Friction loss is the pressure lost to turbulence and drag as water moves through hose. It depends on three things: the hose diameter (expressed as a coefficient), how much water is flowing, and how long the lay is.

Here C is the hose coefficient, Q is flow in hundreds of gallons per minute (150 gpm becomes 1.5), and L is length in hundreds of feet (200 ft becomes 2). The coefficient for the two most common attack lines is 15.5 for 1¾-inch and 2 for 2½-inch. The full coefficient chart, the metric form of the formula, and the reasoning behind it are in the friction loss guide. For this article you only need the two coefficients above.

The flow term is squared, which is the whole reason friction loss catches people out. Doubling the flow does not double the friction loss. It quadruples it.

Elevation pressure (EL)

Water weighs something. Lifting it costs pressure, and letting it fall gives pressure back. A column of water 1 ft tall exerts 0.434 psi at its base, and 1 m of water exerts 9.81 kPa. That is the exact figure, and it is the one the Fire Pump Simulator engine uses.

On the fireground, operators use a rounded rule:

• 0.5 psi per foot of elevation, or 10 kPa per metre
• 5 psi per storey above the first floor, or 35 kPa per storey

A nozzle on the fourth floor is three storeys above the pump, so elevation pressure is 3 × 5 = 15 psi (about 105 kPa). A nozzle 40 ft up a hillside needs 0.5 × 40 = 20 psi. A nozzle 20 ft below the pump, down an embankment, gets 10 psi of free pressure, so elevation pressure is minus 10 psi.

The rounded rule overstates the loss slightly, which errs on the side of a stronger stream. Use the exact figure when you want to check your work against a calculator or the simulator, and the rounded rule at the panel.

Appliance loss (AL)

Every device water passes through adds turbulence. The standard IFSTA allowances are:

• 0 psi for any appliance when total flow is under 350 gpm (1,325 L/min)
• 10 psi (70 kPa) for each wye, siamese, or other appliance when flow is 350 gpm or more
• 25 psi (175 kPa) for master stream appliances such as deck guns, portable monitors, and ladder pipes, regardless of flow

A single 1¾-inch handline running through a gated wye at 150 gpm has no appliance loss. Two 1¾-inch lines flowing 150 gpm each through the same wye total 300 gpm, still no appliance loss. Push them to 185 gpm each and the total is 370 gpm, so the wye costs you 10 psi.

Worked example 1: a single 1¾-inch attack line

The most common evolution there is. One 1¾-inch (45 mm) line, 200 ft (60 m) long, with a fog nozzle flowing 150 gpm (570 L/min) at ground level with no appliances.

1. Nozzle pressure. Fog nozzle, so NP = 100 psi.
2. Friction loss. C = 15.5, Q = 1.5, L = 2. FL = 15.5 × 1.5² × 2 = 15.5 × 2.25 × 2 = 69.75 psi. Round to 70 psi.
3. Elevation. Ground level, so EL = 0.
4. Appliances. None, and flow is under 350 gpm anyway, so AL = 0.

PDP = 100 + 70 + 0 + 0 = 170 psi.

In metric, with the coefficient table in hundreds of litres per minute and hundreds of metres: C = 24.5, Q = 5.7, L = 0.6. FL = 24.5 × 5.7² × 0.6 = 24.5 × 32.49 × 0.6 = 478 kPa, call it 480 kPa. PDP = 700 + 480 = 1,180 kPa. The two answers agree once you convert (170 psi is 1,172 kPa).

Worked example 2: a 2½-inch line with a smooth bore

A 2½-inch (65 mm) line, 300 ft (90 m) long, with a 1⅛-inch smooth bore tip at 50 psi, ground level, no appliances.

Smooth bore nozzles do not come with a flow printed on the box, so start by finding the flow. The smooth bore flow formula is Q = 29.7 × d² × √NP, where d is the tip diameter in inches:

Q = 29.7 × 1.125² × √50 = 29.7 × 1.266 × 7.07 = 266 gpm. Most operators round this to 265 gpm and move on.

1. Nozzle pressure. Smooth bore handline, NP = 50 psi.
2. Friction loss. C = 2, Q = 2.66, L = 3. FL = 2 × 2.66² × 3 = 2 × 7.08 × 3 = 42.4 psi. Round to 42 psi.
3. Elevation and appliances. Zero.

PDP = 50 + 42 = 92 psi.

Notice how low that is. A 2½-inch line moves nearly twice the water of the 1¾-inch line in example 1 at little more than half the pump pressure. Hose diameter is the strongest lever you have against friction loss, which is why 2½-inch hose is the right call for big fire and long stretches.

Worked example 3: a line to the third floor

Same 1¾-inch line as example 1, but 150 ft (45 m) long, flowing 150 gpm (570 L/min), with the nozzle operating on the third floor.

1. Nozzle pressure. 100 psi.
2. Friction loss. C = 15.5, Q = 1.5, L = 1.5. FL = 15.5 × 2.25 × 1.5 = 52.3 psi. Round to 52 psi.
3. Elevation. The third floor is two storeys above the pump. EL = 2 × 5 = 10 psi. (The exact figure, at roughly 10 ft per storey, is 0.434 × 20 = 8.7 psi. The rule of thumb is close enough and slightly conservative.)
4. Appliances. None.

PDP = 100 + 52 + 10 = 162 psi.

In metric: FL = 24.5 × 5.7² × 0.45 = 358 kPa, EL = 2 × 35 = 70 kPa, PDP = 700 + 358 + 70 = 1,128 kPa, or about 1,130 kPa.

Worked example 4: a 65 mm line in metric

A 65 mm (2½-inch) line, 90 m (300 ft) long, with a fog nozzle flowing 950 L/min (250 gpm) at ground level.

1. Nozzle pressure. Fog nozzle, 700 kPa.
2. Friction loss. Metric C for 65 mm is 3.16, Q = 9.5, L = 0.9. FL = 3.16 × 9.5² × 0.9 = 3.16 × 90.25 × 0.9 = 257 kPa.
3. Elevation and appliances. Zero.

PDP = 700 + 257 = 957 kPa, call it 960 kPa.

The imperial version: C = 2, Q = 2.5, L = 3. FL = 2 × 6.25 × 3 = 37.5 psi. PDP = 100 + 37.5 = 137.5 psi, which is 948 kPa. Again the two systems agree within rounding.

Pumping more than one line

A pump has one discharge pressure and many discharge valves. When two lines need different pressures, you set the pump for the line that needs the most pressure and then throttle, or "gate," the other discharges down until each line's own gauge reads what that line needs.

Say line A is the 1¾-inch line from example 1 and needs 170 psi. Line B is the 2½-inch smooth bore from example 2 and needs 92 psi. You bring the pump up to 170 psi, open B's discharge, and ease it closed until B's individual gauge reads 92. The master gauge stays at 170. If you set the pump to 92 to satisfy B, line A gets a limp stream and the crew on it finds out the hard way.

Two rules make this manageable:

• Open the highest-pressure line first and set the pump for it. Adding lower-pressure lines afterward only requires gating.
• Watch the individual discharge gauges, not just the master. Each one tells you what that line is actually getting.

Gating works because the surplus pressure is burned across the partially closed valve. The risk is that valve being opened further by mistake, which puts full pump pressure on a line or device that cannot take it, such as a standpipe or an appliance with a maximum rated pressure.

Mistakes that show up on exams and the fireground

Forgetting to square the flow. FL = C × Q × L gives you a friction loss that is far too low at high flows. The flow term is squared.

Using feet instead of hundreds of feet. With L = 200 instead of 2, the answer is a hundred times too big and clearly wrong. Smaller unit slips are harder to spot.

Adding elevation when the nozzle is below the pump. Downhill gives pressure back. Subtract it.

Adding appliance loss at low flow. A wye on a 150 gpm line costs nothing in the standard method.

Mixing coefficient conventions. The imperial coefficients (15.5, 2, and so on) go with Q in hundreds of gpm and L in hundreds of feet. The metric coefficients (24.5, 3.16) go with Q in hundreds of L/min and L in hundreds of metres. Do not mix them.

Setting the pump for the wrong line. The pump serves the hungriest line. Everything else gets gated.

Practice this

Reading the formula and running it under stress are different skills. A few ways to close that gap:

• Run the numbers above through the free pump discharge pressure calculator. It uses the same friction loss coefficients as the simulator, so it is a good check on your arithmetic. It covers nozzle pressure, friction loss and elevation; add any appliance loss yourself.
• Open the Fire Pump Simulator sandbox, charge the stock 200 ft 1¾-inch attack line, and watch the gap between the pump discharge gauge and the pressure at the tip. Turn on the inline tip readout in the simulator settings to see nozzle pressure live. That gap is friction loss.
• The free handline job performance requirement in the simulator scores the whole sequence from a cold rig to a sustained, pressurized stream. Run it until the setup is routine, so your attention at the panel is free for the math.
• If you are preparing for a certification exam, the NFPA 1002 study guide covers how PDP questions are framed on the written test, and the practice test has a bank of them.

PDP is the foundation under every other pump calculation. Relay pressures, standpipe pressures, and master stream setups are all this same formula with different numbers plugged in. Get the four terms straight and the rest follows.