How to Calculate Nozzle Flow Rate

Nozzle Flow Rate Calculator

Calculating the flow rate of a nozzle is a critical task in fluid dynamics, essential for industries ranging from fire protection and agriculture (irrigation sprayers) to industrial pressure washing. Determining the correct volume of water passing through an orifice ensures system efficiency, safety, and proper resource management.

The flow rate is primarily determined by the size of the nozzle's opening (orifice area), the pressure of the fluid supplied to the nozzle, and the efficiency of the nozzle shape (discharge coefficient).

The Nozzle Flow Rate Formula

To calculate the flow rate for water through a circular orifice, we use a derivation of Bernoulli's principle. For practical engineering purposes in the United States using imperial units, the formula is:

Q = 29.83 × Cd × d² × √P

Where:

• Q = Flow rate in Gallons Per Minute (GPM)
• Cd = Discharge Coefficient (efficiency of the nozzle)
• d = Diameter of the nozzle orifice in inches
• P = Pressure at the nozzle inlet in Pounds per Square Inch (PSI)
• 29.83 = A constant factor that incorporates gravity and unit conversions

Note on Discharge Coefficient (Cd): No nozzle is 100% efficient. Friction and turbulence reduce the flow. A perfect nozzle would have a Cd of 1.0. Most smooth bore fire nozzles range between 0.96 and 0.98. Standard spray nozzles may be lower, around 0.90 to 0.95.

Step-by-Step Calculation Example

Let's calculate the flow rate for a pressure washer tip or a fire hose nozzle with the following specifications:

• Nozzle Diameter: 0.5 inches
• Pressure: 60 PSI
• Discharge Coefficient: 0.97 (Smooth bore)

Step 1: Square the Diameter

First, calculate the square of the diameter ($d^2$):

$$0.5 \times 0.5 = 0.25$$

Step 2: Find the Square Root of Pressure

Next, find the square root of the pressure ($\sqrt{P}$):

$$\sqrt{60} \approx 7.746$$

Step 3: Apply the Formula

Now multiply all the components together:

$$Q = 29.83 \times 0.97 \times 0.25 \times 7.746$$

$$Q \approx 56.03 \text{ GPM}$$

Understanding the K-Factor

In fire protection engineering and irrigation, nozzles are often rated by a "K-Factor." The K-Factor simplifies the relationship between pressure and flow. If you know the K-Factor, the formula becomes even simpler:

Q = K × √P

Our calculator above estimates the K-Factor based on your diameter and coefficient inputs. This helps in quickly estimating flow changes when only the pressure changes.

Why Velocity Matters

The calculator also provides the fluid velocity in feet per second (ft/s). Velocity helps determine the "reach" of a stream (how far the water will travel). High pressure with a small diameter creates high velocity, ideal for cleaning or long-range firefighting, while low pressure with a large diameter provides volume (GPM) without the force, ideal for gentle irrigation.