A centrifugal pump compresses 3000 liters/min of water from 98 KPa to 300KPa. the inlet and outlet temp are 25°C. The inlet and discharge pipe are on the same level but the diameter of the inlet piping is 15cm whereas that of the discharge piping is 10cm. Determine the pump work in kW
Calculate the inlet and outlet velociies V1 and V2 using the contiuity equation
V * A = 3000 liters/min = 3*10^6 cm^3/min
A1 = pi*(15)^2 = 706.9 cm^2
A2 = pi*(10)^2 = 314.2 cm^2
V1 = 3*10^6/706.9
= 4244 cm/s = 42.44 m/s
V2 = 95.48 m/s
The steady state energy equation says that
Mdot*(U + P*v + KE + PE)out = Mdot*(U + P*v+ KE+ PE)in + (Power)in
Mdot is the mass flow rate
U is the internal energy, which does not change because inlet and outlet temperatures are equal. KE(per mass) = V^2/2. PE is potential energy which does not change since the inlet and outlet are at the same elevation. P v
is pressure times specific volume, which is the same as pressure divided by density.
The energy equation simplifies to:
Power in = Mdot*[P/density + V^2/2]out -Mdot*[P/density + V^2/2]in
For water, density = constant = 1000 kg/m^3
Mdot = 3 m^3/min * 1000 kg/m^3 = 3000 kg/min = 50 kg/s
First let us calculate the power needed to increase the pressure.
Mdot*(Pout-Pin)/density
= 50 kg/s*(202*10^5 N/m^2)/1000 kg/m^3
= 60.6*10^6 J/s = 1.01 Megawatts
You need to add to that the additional power needed to increase the kinetic energy
Mdot*[V2^2/2 - V1^2/2]
Take it from there and check my numbers.
A centrifugal pump compresses 3000 liters/min of water from 98 KPa to 300KPa. the inlet and outlet temp are 25°C. The inlet and discharge pipe are on the same level but the diameter of the inlet piping is 15cm whereas that of the discharge piping is 10cm. Determine the pump work in kW
To determine the pump work in kW, we need to calculate the change in specific enthalpy (Δh) of the water being pumped. The pump work is then given by the product of the mass flow rate (ṁ) and Δh.
Step 1: Calculate the mass flow rate (ṁ) of water:
Given:
- Volume flow rate = 3000 liters/min
To convert liters to cubic meters, divide by 1000:
- Volume flow rate = 3000/1000 = 3 m^3/min
The density of water at 25°C is approximately 1000 kg/m^3. Therefore:
- Mass flow rate (ṁ) = volume flow rate * density
= 3 * 1000
= 3000 kg/min
Step 2: Calculate the change in specific enthalpy (Δh):
Given:
- Inlet pressure (P1) = 98 kPa
- Outlet pressure (P2) = 300 kPa
To calculate Δh, we need to determine the enthalpy values at both the inlet and outlet conditions.
Using a water property table or software, we can find the enthalpy corresponding to the inlet pressure (P1) and temperature (T):
- P1 = 98 kPa and T = 25°C
- Inlet enthalpy (h1) = water enthalpy at P1, T (from the table)
Similarly, for the outlet pressure (P2) and temperature (T):
- P2 = 300 kPa and T = 25°C
- Outlet enthalpy (h2) = water enthalpy at P2, T (from the table)
Step 3: Calculate the pump work:
- Δh = (h2 - h1)
Finally, using the equation for pump work:
- Pump work = mass flow rate * Δh
Note: The specific enthalpy values obtained from the tables will likely be in kJ/kg. You will need to convert the mass flow rate and Δh to the appropriate units (kg/min and kJ) before calculating the pump work. Once you have the pump work value, convert it to kW by dividing by 1000.
Please consult a water property table or water properties software to obtain the specific enthalpy values at the given pressures and temperatures.
To determine the pump work in kW, we need to use the following relationship:
Pump Work = Pump Power x Time
The pump power can be calculated using the following formula:
Pump Power = (Flow Rate x Pressure Change) / Pump Efficiency
First, let's calculate the flow rate (Q) in m^3/s:
Q = Flow Rate / 1000 (convert liters to cubic meters)
Q = 3000 / 1000 = 3 m^3/min
Next, let's calculate the pressure change (ΔP) in Pascals:
ΔP = Outlet Pressure - Inlet Pressure
ΔP = (300 KPa - 98 KPa) x 1000 (convert KPa to Pa)
ΔP = 202,000 Pa
Now, let's calculate the pump efficiency (η). The efficiency of a centrifugal pump typically ranges from 0.70 to 0.90. Let's use a conservative estimate of 0.70:
η = 0.70
Now, let's calculate the pump power (P) in Watts:
P = (Q x ΔP) / η
P = (3 m^3/min x 202,000 Pa) / 0.70
P = 866,000 W
Finally, let's convert the pump power from Watts to kilowatts:
Pump Power (kW) = P / 1000
Pump Power (kW) = 866,000 W / 1000
Pump Power (kW) = 866 kW
Therefore, the pump work is 866 kW.