Answer :
The estimated pressure loss for a 5 m length of the pipe is approximately 17.30 kPa.
To estimate the pressure loss in kPa for a 5 m length of the pipe, we can use the Darcy-Weisbach equation.
First, let's convert the volumetric flow rate from gallons per minute (gpm) to cubic meters per second (m³/s). Since 1 gallon is approximately equal to 0.00378541 cubic meters, we can use this conversion factor:
2,200 gpm * 0.00378541 m³/gallon * (1/60) min/s = 2.325 m³/s
Next, let's calculate the average velocity of the water in the pipe. We can do this by dividing the volumetric flow rate by the cross-sectional area of the pipe. The cross-sectional area can be calculated using the inside diameter of the pipe:
Inside diameter = 18 inches
= 0.4572 meters
Radius = 0.4572 / 2
= 0.2286 meters
Cross-sectional area = π * (0.2286)²
= 0.16413 m²
Average velocity = 2.325 m³/s / 0.16413 m²
= 14.165 m/s
Now, we can use the Darcy-Weisbach equation to calculate the pressure loss:
Pressure loss = (f * (L / D) * (ρ * v²)) / 2
Where:
f is the Darcy friction factor
L is the length of the pipe (5 m)
D is the inside diameter of the pipe (0.4572 m)
ρ is the density of water (1,000 kg/m³)
v is the average velocity of the water (14.165 m/s)
To determine the Darcy friction factor, we need the Reynolds number. The Reynolds number is calculated as the product of the velocity, pipe diameter, and the kinematic viscosity of water (ν), divided by the dynamic viscosity of water (μ). The kinematic viscosity of water is approximately 1.004 × 10⁻⁶ m²/s.
Re = (v * D * ν) / μ
Re = (14.165 m/s * 0.4572 m * 1.004 × 10⁻⁶ m²/s) / 0.001 kg/(m·s)
Re ≈ 64,057
Based on the Reynolds number, we can determine the flow regime. Since the Reynolds number is less than 2,300, the flow in the pipe is laminar.
For laminar flow, the Darcy friction factor (f) can be calculated using the following equation:
f = (64 / Re)
f ≈ (64 / 64,057)
f ≈ 0.001
Now we can substitute the values into the Darcy-Weisbach equation:
Pressure loss = (0.001 * (5 m / 0.4572 m) * (1,000 kg/m³ * (14.165 m/s)²)) / 2
Pressure loss ≈ 17,303.67 Pa
Finally, we can convert the pressure loss from pascals (Pa) to kilopascals (kPa) by dividing by 1,000:
Pressure loss ≈ 17,303.67 Pa / 1,000
Pressure loss ≈ 17.30 kPa
Therefore, the estimated pressure loss for a 5 m length of the pipe is approximately 17.30 kPa.
Learn more about pressure loss visit:
brainly.com/question/31825855
#SPJ11
