FireHydrant-Calculation

Calculating pip flow metrics

Water Jet Height Calculation

Overview

This script calculates the maximum height that a water jet can reach when exiting a hole of varying diameters and under different pressures. It uses Torricelli's Theorem to determine the velocity of the water and subsequently compute the height.

Formulae Used

1. Velocity Calculation (Torricelli’s Theorem)

The velocity of the water exiting the hole is calculated using:

$[ v = \sqrt{\frac{2 P}{\rho}} ]$

Where:

• $( v )$ = velocity of the water (m/s)
• $( P )$ = pressure (Pa)
• $( \rho )$ = density of water (1000 kg/m³)

2. Height Calculation

The height the water jet reaches is given by:

$[ h = \frac{v^2}{2g} ]$

Where:

• $( h )$ = maximum height (m)
• $( g )$ = acceleration due to gravity (9.81 m/s²)

Code Explanation

The function calculate_jet_height(diameter_inches, pressure_psi) takes multiple diameters and multiple pressure values as inputs. It iterates through all combinations and calculates:

• Velocity of water exiting the hole
• Maximum height in meters and feet

Inputs

• diameter_inches: List of hole diameters (in inches)
• pressure_psi: List of water pressures (in PSI)

Outputs

A DataFrame with the following columns:

• Diameter (in): Diameter of the hole in inches
• Pressure (PSI): Pressure in PSI
• Pressure (BAR): Pressure converted to BAR
• Velocity (m/s): Velocity of the water exiting the hole
• Max Height (m): Maximum height in meters
• Max Height (ft): Maximum height in feet

Example Usage

Input

pressure_values = [40, 50, 60, 80, 100]  # PSI values
diameter_values = [0.5, 1.0, 1.5]  # Hole diameters in inches

df_results = calculate_jet_height(diameter_values, pressure_values)
print(df_results)

Expected Output

A DataFrame showing calculated velocities and heights for different diameters and pressures.

Diameter (in)	Pressure (PSI)	Pressure (BAR)	Velocity (m/s)	Max Height (m)	Max Height (ft)
0.5	40	2.76	8.37	3.57	11.7
1.0	40	2.76	8.37	3.57	11.7
1.5	40	2.76	8.37	3.57	11.7
0.5	100	6.90	13.27	8.98	29.4
1.0	100	6.90	13.27	8.98	29.4
1.5	100	6.90	13.27	8.98	29.4

Notes

• Higher pressure results in a greater velocity and higher water spray.
• Larger hole diameters do not affect height but can affect flow rate.

Applications

This calculation is useful for:

• Fire hydrant leakage analysis (e.g., unauthorized openings)
• Municipal water system analysis
• Hydraulic engineering and plumbing design