First, we need to calculate the pressure drop in the system. The Darcy-Weisbach equation can be used to determine the pressure drop:
ΔP = f * (L/D) * (ρ * V^2) / 2
Where:
ΔP = pressure drop (psi)
f = friction factor (depends on Reynolds number, which can be calculated using the flow rate and pipe diameter)
L = length of the pipe (ft)
D = diameter of the pipe (ft)
ρ = density of the fluid (lb/ft^3)
V = velocity of the fluid (ft/s)
First, let's calculate the Reynolds number:
Re = (ρ * V * D) / μ
Where:
μ = viscosity of the fluid (lb/ft*s)
Next, we need to calculate the friction factor using the Colebrook equation:
1 / √f = -2 * log10((ε/D)/3.7 + 2.51 / (Re * √f))
Where ε = roughness of the pipe (assumed to be 0.0005 ft for standard iron pipe)
Now we can calculate the pressure drop using the Darcy-Weisbach equation.
Next, we calculate the total head required at the pump outlet:
Total Head = ΔP + (Z2 - Z1) + (V2^2 - V1^2) / (2 * g)
Where:
Z2 - Z1 = 22 ft
V1 = 20 gpm / (π * (1.25/12)^2 / 4) * (1 / 448.832) = 7.19 ft/s
V2 = 1.5 * V1 = 10.78 ft/s
g = acceleration due to gravity = 32.2 ft/s^2
Now, we calculate the pump output required:
Pump Output = (Q * Total Head) / (η / 0.6)
Where:
Q = 1.5 * 20 gpm = 30 gpm
Now we have all the information we need to calculate the pump output required by the electric motor for this duty.
A 90% by weight solution of methyl alcohol in water is to be pumped from a storage tank to a process department through a 1-1/4 inch standard iron pipe 1450 ft long. The line contains 15 standard elbows, 5 gate valves, 6 tees straight through, and 4 tees through a side outlet. The process end of the line must have a pressure of 8 psig and is 22 feet above the storage tank. The temperature of the line can be taken at 40 degree Fahrenheit as the lowest it will possibly attain, and the flow will be rated at 20 gpm, but it may be over-loaded by 50%. Assuming 60% pump efficiency, calculate the output required by the electric motor to be used for this duty
3 answers
A 90% by weight solution of methyl alcohol in water is to be pumped from a storage tank to a process department through a 1-1/4 inch standard iron pipe 1450 ft long. The line contains 15 standard elbows, 5 gate valves, 6 tees straight through, and 4 tees through a side outlet. The process end of the line must have a pressure of 8 psig and is 22 feet above the storage tank. The temperature of the line can be taken at 40 degree Fahrenheit as the lowest it will possibly attain, and the flow will be rated at 20 gpm, but it may be over-loaded by 50%. Assuming 60% pump efficiency, calculate the output required by the electric motor to be used for this duty
Given information:
- Solution: 90% by weight methyl alcohol in water
- Pipe: 1-1/4 inch standard iron pipe
- Length of pipe: 1450 ft
- Components: 15 standard elbows, 5 gate valves, 6 tees straight through, 4 tees through a side outlet
- Process end pressure: 8 psig
- Process end elevation: 22 ft above storage tank
- Lowest temperature: 40°F
- Rated flow: 20 gpm, can be overloaded by 50%
- Pump efficiency: 60%
To calculate the output required by the electric motor, we need to determine the total head loss in the system and the pump output. Let's start by calculating the pressure drop due to friction in the pipe.
1. Calculate Reynolds Number:
Density of water ρ = 62.4 lb/ft^3, viscosity of water μ = 1.22 lb/(ft*s)
Re = (ρ * V * D) / μ
Re = (62.4 * 30 * π * (1.25/12)^2 / 4) / (1.22)
Re ≈ 46840
2. Calculate Friction Factor:
Using the Colebrook equation, we can determine the friction factor by iteration:
Start with an assumed value of f = 0.02
Calculate a new f using the Colebrook equation
Iterate until convergence is reached
Assuming the friction factor, f ≈ 0.02
3. Calculate Pressure Drop:
ΔP = f * (L/D) * (ρ * V^2) / 2
Convert the flow rate to ft^3/s: Q = 30 gpm / 448.832 = 0.06681 ft^3/s
ΔP = 0.02 * (1450 / (1.25/12)) * (62.4 * 0.06681^2) / 2
ΔP ≈ 63.65 psi
4. Calculate Total Head Required:
Total Head = ΔP + (Z2 - Z1) + (V2^2 - V1^2) / (2 * g)
g = 32.2 ft/s^2
Z2 - Z1 = 22 ft
5. Calculate Pump Output:
Pump Output = (Q * Total Head) / (η / 0.6)
η = 0.6 (Pump efficiency)
Now, substitute the calculated values to get the pump output required by the electric motor for this duty.
- Solution: 90% by weight methyl alcohol in water
- Pipe: 1-1/4 inch standard iron pipe
- Length of pipe: 1450 ft
- Components: 15 standard elbows, 5 gate valves, 6 tees straight through, 4 tees through a side outlet
- Process end pressure: 8 psig
- Process end elevation: 22 ft above storage tank
- Lowest temperature: 40°F
- Rated flow: 20 gpm, can be overloaded by 50%
- Pump efficiency: 60%
To calculate the output required by the electric motor, we need to determine the total head loss in the system and the pump output. Let's start by calculating the pressure drop due to friction in the pipe.
1. Calculate Reynolds Number:
Density of water ρ = 62.4 lb/ft^3, viscosity of water μ = 1.22 lb/(ft*s)
Re = (ρ * V * D) / μ
Re = (62.4 * 30 * π * (1.25/12)^2 / 4) / (1.22)
Re ≈ 46840
2. Calculate Friction Factor:
Using the Colebrook equation, we can determine the friction factor by iteration:
Start with an assumed value of f = 0.02
Calculate a new f using the Colebrook equation
Iterate until convergence is reached
Assuming the friction factor, f ≈ 0.02
3. Calculate Pressure Drop:
ΔP = f * (L/D) * (ρ * V^2) / 2
Convert the flow rate to ft^3/s: Q = 30 gpm / 448.832 = 0.06681 ft^3/s
ΔP = 0.02 * (1450 / (1.25/12)) * (62.4 * 0.06681^2) / 2
ΔP ≈ 63.65 psi
4. Calculate Total Head Required:
Total Head = ΔP + (Z2 - Z1) + (V2^2 - V1^2) / (2 * g)
g = 32.2 ft/s^2
Z2 - Z1 = 22 ft
5. Calculate Pump Output:
Pump Output = (Q * Total Head) / (η / 0.6)
η = 0.6 (Pump efficiency)
Now, substitute the calculated values to get the pump output required by the electric motor for this duty.
4 answers