#1. A centrifugal pump compresses 50 kg/sec of water adiabatically from 98 kPaa to 300 kPaa. The inlet and outlet temperatures are at 25 oC. The Inlet and discharge piping are at the same level (ΔPe=0), but the diameter of the inlet piping is 15 cm, where as that of the discharge piping is 10 cm. Determine the pump power in kilowatts. The density of water is 1000 kg/m3
To determine the pump power in kilowatts, we need to calculate the work done by the pump.
The work done by the pump can be calculated using the formula:
Work (W) = m_dot * Cp * (T_discharge - T_inlet)
Where:
- m_dot is the mass flow rate of water (in kg/sec)
- Cp is the specific heat capacity of water (in J/kg·K)
- T_discharge is the discharge temperature (in Kelvin)
- T_inlet is the inlet temperature (in Kelvin)
Let's calculate the values needed to find the work done by the pump:
1. Calculate the mass flow rate:
m_dot = 50 kg/sec
2. Convert the inlet and discharge temperatures to Kelvin:
T_inlet = 25 + 273.15 = 298.15 K
T_discharge = 25 + 273.15 = 298.15 K (assuming no significant change in temperature)
3. Determine the specific heat capacity of water (Cp):
Cp = 4,184 J/kg·K (specific heat capacity of water at room temperature)
Substituting the values into the equation:
Work (W) = 50 kg/sec * 4,184 J/kg·K * (298.15 K - 298.15 K)
= 0 J
Since the inlet and discharge temperatures are the same (no change in temperature), the work done by the pump is zero. Therefore, the pump power is also zero kilowatts.
Note: If there was a change in temperature, we would need to account for the change in enthalpy and use the appropriate value for Cp. However, in this case, since the inlet and discharge temperatures are the same, the work done is zero.