To determine the flow volume from a nozzle, you can use the formula derived from the orifice flow equation, assuming that the flow is water or a similar fluid with similar properties. The equation typically used for flow through a nozzle is:

$Q = C_d A \sqrt{2 g h}$

Where:

• $Q$ = flow rate (gallons per minute, GPM or liters per minute, LPM)
• $C_d$ = discharge coefficient (typically between 0.6 and 1.0 for most nozzles)
• $A$ = cross-sectional area of the nozzle (in square inches or square millimeters)
• $g$ = acceleration due to gravity ($9.81 \, m/s^2$)
• $h$ = pressure head, which is the pressure in feet or meters of head

Steps:

1. Convert the given pressure (80 psi) into feet of head:

   The pressure head $h$ is related to the pressure $P$ in psi as follows:

   $h = \frac{P \times 2.31}{\rho}$

   Where:

   • $P = 80 \, \text{psi}$
   • $\rho = 1.0 \, \text{(unitless for water)}$

   So, $h \approx 80 \times 2.31 = 184.8 \, \text{ft of head}$.

2. Calculate the nozzle area $A$:

   The diameter of the nozzle is given as ¼ inch (which is approximately 0.25 inches). The area of the nozzle's opening is calculated using the formula for the area of a circle:

   $A = \pi \left(\frac{d}{2}\right)^2$

   Where $d = 0.25 \, \text{inches}$, so:

   $A = \pi \left(\frac{0.25}{2}\right)^2 = \pi (0.125)^2 \approx 0.0491 \, \text{in}^2$

3. Calculate the flow rate $Q$:

   Now we can apply the flow equation. Assuming a typical discharge coefficient $C_d = 0.9$ for a solid stream nozzle:

   $Q = 0.9 \times 0.0491 \times \sqrt{2 \times 32.2 \times 80} \approx 0.9 \times 0.0491 \times 50.72$

   $Q \approx 2.81 \, \text{GPM} \quad (\text{gallons per minute})$

Final Flow Rate:

The flow rate is approximately 2.81 gallons per minute (GPM).

---

Would you like further details or have additional questions about the calculation? Here are some related questions to consider:

1. How would the flow rate change if the nozzle size increases?
2. What happens to the flow rate if the pressure is reduced to 60 psi?
3. How does fluid viscosity affect the flow rate through a nozzle?
4. What is the impact of nozzle material on the flow rate calculation?
5. Can this method be used for gases as well as liquids?

Tip: Always check the manufacturer's specifications for exact discharge coefficients for your nozzle type, as these can vary significantly depending on design.