Pump

Under construction.

Performance

The following performance calculations are available on pump instances.

Calculation Reference Output Tags
Pump Efficiency   .efficiency.use

Calculations

Efficiency

Pump efficiency is defined as:

$$\eta _{pump} = \frac{Q_{fw}}{Q_{i}} = \frac{Q_{fw}}{Q_{fw} + Q_{loss}}$$

Where:

  • $Q_{fw}$ = Pump feedwater power
  • $Q_{i}$ = Pump input drive power
  • $Q_{loss}$ = Pump losses

In CAS terms:

$$pump.efficiency.use = \frac{pump.fluidPower.use}{pump.c2in.energyFlow.use} = \frac{pump.fluidPower.use}{pump.fluidPower.use + pump.c2in.energyFlow.use}$$

Feedwater Power

The pump feedwater power (Bernoulli) is given by:

$$Q_{fw} = \left ( \frac{P_{o}}{\rho} + z_{o}.g + \frac{v_{o}^{2}}{2} \right ) - \left ( \frac{P_{i}}{\rho} + z_{i}.g + \frac{v_{i}^{2}}{2} \right )$$

Where:

  • $P_{i/o}$ = Inlet/outlet pressure
  • $z_{i/o}$ = Inlet/outlet elevation (= 0 if no static pressure correction is required)
  • $v_{i/o}$ = Inlet/outlet flow velocity
  • $g$ = $$9.81 m/s^{2}$$
  • $\rho$ = Density
  • Note: pipe diameters will also be required to determine flow velocity.

In CAS terms (where ”.” represents the pump):

$$pump.fluidPower.use = \left ( \frac{.c1out.prop.press.use}{.c1out.prop.density.use} + .outlet.elevation \times 9.81 + .outlet.velocity^{2} \right ) - \left ( \frac{.c1out.prop.density.use}{.c1in.prop.density.use} + .inlet.elevation*9.81 + \frac{.inlet.velocity^{2}}{2} \right )$$

Losses

If pump input drive power $$P_{i}$$ cannot be determined directly then pump efficiency can be derived by determining the pump losses. Losses are determined by calculating the enthalpy rise of the feedwater across the pump.

$$H_{loss} = H_{fw_{o}} - H_{fw_{i}}$$

Where:

  • $H_{loss}$ = Pump loss due to feedwater enthalpy rise
  • $H_{fw_{i/o}}$ = Inlet/outlet enthalpy of the feedwater

In CAS terms:

$$pump.c1.dQ.use = pump.c1out.prop.energy.use - pump.c1in.prop.energy.use$$

Turbine Pump Drive Power

If the pump is turbine driven the pump input drive power is given by:

$$Q_{i} = \frac{m_{t}(H_{i} - H_{o})} {m_{fw}}$$

Where:

  • $m_{t}$ = Turbine steam massflow
  • $m_{fw}$ = Feedwater massflow
  • $H_{i/o}$ = Turbine inlet/outlet enthalpy

In CAS terms:

$$pump.c2in.energyFlow.use = pump.c2in.massFlow.use \times (pump.c2out.prop.energy.use - pump.c1in.prop.energy.use)$$

Motor Pump Driver Power

If the pump is motor driven the pump input drive power is given by:

$$Q_{i} = \sqrt{3} \times V \times i \times cos\phi$$

Where:

  • $V$ = Motor voltage
  • $i$ = Motor current
  • $cos\phi$ = Power factor

In CAS terms:

$$motor.c2in.energyFlow.use = \sqrt{3} \times motor.volts.use \times motor.current.use \times motor.powerFactor.use$$

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