Welcome to the Online Calculations for Plunger Pumps and High-Pressure Nozzles

Your support for the sizing and efficiency improvement of plunger pumps and high-pressure nozzles.

Simple and Accurate Plunger Pump – Calculations

On this page, you will find essential formulas and calculation basics to determine the required drive power and optimize the operation of your high-pressure pumps and nozzles. These formulas allow you to precisely calculate the following parameters:

  • Required Drive Power
  • Maximum Allowable Pressure
  • Theoretical Flow Rate
  • Rod Force
  • Nozzle Size and Performance

High-Pressure Nozzle – Calculator

In addition, we offer a special nozzle calculator to help you determine the ideal nozzle size and performance for your high-pressure applications.

Amount image for plunger pump calculations on the KAMAT website. You can see a parts list of a high-pressure pump

Formulas

Plunger Speed
▲
Formula
Variables & Calculation
\( { \textcolor{#cc0000}{v_{pl}} } = \textcolor{#009a25}{s} \cdot { \textcolor{#067fb2}{n} \over {30} } \)
Variables & Calculation
Stroke
s
=
m
Speed
n
=
rpm
Plunger speed
vpl
=
m/s
The plunger speed in a high-pressure pump is a critical factor in the power density and life of the pump. The higher the piston speed, the smaller the pump for the same performance. The lower the piston speed, the less wear on the pump. Plunger speed is calculated using the following formula: v is the plunger speed, s is the plunger stroke in metres and n is the number of crankshaft revolutions per minute. This formula gives the average piston speed, which is how fast the piston moves back and forth in a given unit of time. This speed is a critical factor in the volume of liquid pumped. An optimised plunger speed ensures effective and efficient fluid delivery with appropriate wear. A plunger that is too fast can lead to increased wear, while a plunger that is too slow will reduce pumping capacity.
Input Torque of a Triplex Pump
▲
Formula
Variables & Calculation
\( { \textcolor{#cc0000}{M} } = { \textcolor{#009a25}{P} ~ \cdot ~ 1000 \over \textcolor{#067fb2}{ω} } \)
Variables & Calculation
Input power
P
=
kW
Shaft frequency
ω
=
1/s
Torque
M
=
Nm
The input torque of a pump is a characteristic value that describes the transfer of mechanical energy from the drive source to the pump itself.

The formula shows that the torque required is inversely proportional to speed, which means that at higher speeds less torque is required to achieve the same performance. This is particularly important when selecting and sizing drive motors in pumping systems to ensure that the motor operates efficiently and meets the specified requirements.

However, for a given pressure, the torque required by a plunger pump is constant over the entire speed range!
Drive Power of a Pump
▲
Formula
Variables & Calculation
\( { \textcolor{#cc0000}{P} } = { \textcolor{#009a25}{M} ~ \cdot ~ \textcolor{#067fb2}{ω} \over 1000 } \)
Variables & Calculation
Torque
M
=
Nm
Shaft frequency
ω
=
1/s
Input power
P
=
kW
The drive power of a pump is a measure of the power that must be supplied to the pump by the drive source to produce the required pressure and flow.

The above formula can be used to determine the required drive power for a pump if the required torque and angular frequency (angular velocity) are known. This is particularly useful for engineers and technicians designing or analyzing pump systems to ensure that the drive motor is suitable and properly sized to provide the required power at the specified speed.

However, for a given pressure, the required torque of a plunger pump is constant over the entire speed range.

To accurately calculate drive power, it is important to know the actual torque required by the pump at a given operating speed, as well as any factors that may affect the efficiency of the system.
Angular Speed
▲
Formula
Variables & Calculation
\( { \textcolor{#cc0000}{ω} } = { {\pi} \over {30} } \cdot \textcolor{#009a25}{n} \)
Variables & Calculation
Speed
n
=
1/min
Shaft frequency
ω
=
1/s
The formula for calculating the angular velocity ω from the rotational speed (rpm) helps to determine the rotational speed in a unit useful for physical calculations (radians per second). This calculation is essential to accurately calculate the drive power of a pump or other rotating system.
Input Power at 87.5% Efficiency
▲
Formula
Variables & Calculation
\( { \textcolor{#cc0000}{P} } \approx \textcolor{#009a25}{Q} \cdot { \textcolor{#067fb2}{p} \over {520} } \)  
Variables & Calculation
Flow rate
Q
=
l/min
Pressure
p
=
bar
Input power
P
≈
kW
This formula for the required input power of a plunger pump makes it possible to calculate the required drive power of the drive motor to produce the desired flow Q and pressure p, taking into account the efficiency of the pump. In other words, it indicates how much power the drive motor must deliver for the pump to operate at the desired duty point under the conservative assumption that the efficiency of the pump is 87.5%. The factor 520 is used to convert the power into kilowatts using the standard industrial units of l/min and bar. In reality, plunger pumps achieve efficiencies of up to 95%, so this formula will always result in a slight oversizing of the drive motor.
Theoretical Flow Rate
▲
Formula
Variables & Calculation
\( { \textcolor{#cc0000}{Q} } = 1000 \cdot \pi \cdot { \textcolor{#009a25}{D}^2 \over {4} } \cdot \textcolor{#067fb2}{s} \cdot \textcolor{#c87400}{n} \cdot \textcolor{#9024b3}{z} \)  
Variables & Calculation
Plunger diameter
D
=
m
Stroke
s
=
m
Speed
n
=
1/min
Number of plunger
z
=
Flow rate
Q
=
l/min
This formula calculates the theoretical flow rate of a plunger pump based on geometric data such as plunger diameter, stroke length, speed and number of plungers. The flow rate, Q, indicates how much fluid the pump can deliver per minute under ideal conditions.

The formula therefore indicates the theoretical flow rate of the pump under ideal conditions, without taking into account efficiency losses due to installation, valve losses, friction or compressibility of the liquid. In practice, the actual flow rate will be less than the theoretical flow rate.
Plunger Force
▲
Formula
Variables & Calculation
\( { \textcolor{#cc0000}{F_{st}} } = \pi \cdot { \textcolor{#009a25}{D}^2 \over {4} } \cdot \textcolor{#067fb2}{p} \cdot 100,000 \)
Variables & Calculation
Plunger diameter
D
=
m
Pressure
p
=
bar
Rod force
Fst
=
N
Water jet impulse is a critical factor in the effectiveness of high-pressure cleaning processes because it describes the momentum with which the water jet hits a surface. The impulse I of a jet is calculated using the following formula, where m is the mass and v is the velocity of the impinging water. This momentum transfers a significant amount of energy to the material being removed and helps to effectively remove dirt, oil or other debris. A higher mass or velocity increases the impulse and therefore the cleaning energy of the jet, which is especially important when removing stubborn or highly adhesive contaminants.

The velocity of the fluid as it strikes the material (impulse) determines whether the material can be removed. This velocity is quadratically related to the pressure in front of the nozzle (and its efficiency). If the material can be removed, this is called the critical pressure in front of the nozzle. The fluid mass per time is linearly related to the removal rate. Therefore, if you want to double the removal rate, you must either double the flow (= double the drive power) or quadruple the working pressure (= quadruple the drive power).
Maximum Allowable Discharge Pressur
▲
Formula
Variables & Calculation
\( { \textcolor{#cc0000}{p_{max}} } = { \textcolor{#009a25}{ {F}_{ {st ~ max}} } \over { \pi ~ \cdot ~ { \textcolor{#067fb2}{D}^2 \over {4} } ~ \cdot ~ 100,000} } \)
Variables & Calculation
Maximum permitted rod force
Fst max
=
N
Plunger diameter
D
=
m
Maximum delivery pressure
pmax
=
bar
To calculate the nozzle diameter (using a conservative efficiency of 81%), the relationship between flow rate, discharge pressure, and nozzle efficiency is used. The nozzle diameter d can be determined using the equation where Q is the flow rate and p is the working pressure upstream of the nozzle. Nozzle efficiency is critical because it determines the velocity of the free jet at the same pressure. The better the nozzle efficiency, the more effectively the fluid pressure is converted into velocity and thus into cleaning performance. A properly sized nozzle diameter/efficiency will ensure that the full flow of the pump is utilized with the least amount of energy loss.
Fluid Speed
▲
Formula
Variables & Calculation
\( \textcolor{#cc0000}{v} = \sqrt{ 20 \cdot 9.81 \cdot \textcolor{#009a25}{p} } \)  
Variables & Calculation
Pressure
p
=
bar
Speed
v
=
m/s
The fluid speed in the free jet after the nozzle is critical to the effectiveness of the high pressure cleaning process.

The speed of the fluid after it leaves the nozzle determines what materials the jet can remove. A higher fluid velocity can remove or even cut harder deposits.
Water Jet Impulse
▲
Formula
Variables & Calculation
\( \textcolor{#cc0000}{I} = \textcolor{#009a25}{m} \cdot \textcolor{#067fb2}{v} \)
Variables & Calculation
Mass
m
=
kg
Speed
v
=
m/s
Impulse
I
=
Ns
The water jet impulse is a critical factor in the effectiveness of high-pressure cleaning processes, as it describes the energy with which the water jet strikes a surface. The impulse I of a jet is calculated using the following formula, where m is the mass and v is the velocity of the impinging water. This impulse transfers a considerable amount of energy to the material being removed and helps to effectively remove dirt, oil or other deposits. A higher mass or velocity increases the impulse and therefore the cleaning energy of the jet, which is particularly important when removing stubborn or highly adhesive contaminants.

The velocity of the fluid as it strikes the material (impulse) determines whether the material can be removed. This velocity is quadratically related to the pressure in front of the nozzle (and its efficiency). If the material can be removed, this is referred to as the critical pressure in front of the nozzle. The mass of fluid per time is a linear function of the removal rate. So if you want to double the removal rate, you must either double the flow rate (= double the drive power) or quadruple the working pressure (= quadruple the drive power)!
Nozzle diameter
▲
Formula
Variables & Calculation
\( \textcolor{#cc0000}{d} \approx \sqrt[4]{2.77 \cdot {\textcolor{#009a25}{Q}^2 \over \textcolor{#067fb2}{p} } }\)  
Variables & Calculation
Flow
Q
=
l/min
Pressure
p
=
bar
Nozzle diameter
d
≈
mm
To calculate the nozzle diameter (using a conservative efficiency of 81%), the relationship between flow rate, discharge pressure and nozzle efficiency is used. The nozzle diameter d can be determined using the equation where Q is the flow rate and p is the working pressure upstream of the nozzle. Nozzle efficiency is critical because it determines the velocity of the free jet at the same pressure. The better the nozzle efficiency, the more effectively the fluid pressure is converted into velocity and thus into cleaning performance. Precisely dimensioned nozzle diameter/efficiency ensures that the full flow of the pump is utilised without wasting energy.

Variables

d Nozzle diameter mm
D Plunger diameter m
Fst Rod force N
Fst max Maximum permitted rod force N
g Gravitational acceleration m/s2
I Impulse Ns
m Mass kg
M Torque Nm
n Speed rpm
p Pressure bar
P Input power kW
pmax Maximum delivery pressure bar
Q Flow rate l/min
s Stroke m
v Speed m/s
vpl Plunger speed m/s
z Number of plunger
ω Shaft frequency 1/s

These plunger pump calculations provide you with an advanced technical resource for optimizing the sizing and efficiency of plunger pumps and high-pressure nozzles.

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Theoretical Calculation Principles and Disclaimer

Please note that the results are based on theoretical assumptions and are for guidance only. You, as the user, are responsible for the correct application and interpretation of the results. KAMAT assumes no responsibility for the accuracy of the data or its use in your projects.

Nozzle calculator for high pressure nozzles

We also offer a special nozzle calculator to help you determine the ideal nozzle size and performance for your high pressure applications.

Take advantage of this opportunity to efficiently design and operate your plunger pumps and high pressure nozzles. Start your calculations online now and increase the efficiency of your systems!