Answer:

The pump work can be simply calculated by using the formula Wpump = Hout - Hin

which is Wp = H4 - H3 in the following case. The enthalpy at the pump inlet can be easily found using the steam tables, which is nothing but saturated liquid enthalpy on the low-pressure line. The problem is it is not easy to calculate the enthalpy at the exit of the pump H4 as it is in the compressed liquid region.

So, we can not directly use Wp = H4 - H3 formula to calculate pump work as we don't know H4 yet.

Hence, here we use one of the four core thermodynamic relations (called Gibbs relations)

dh = Tds+vdp

In the Rankine cycle, the pump is assumed to be isentropic hence the term Tds vanishes. We remain with the equation

dh = vdp.

When the above equation is integrated between states 3 and 4, the pump work can be derived as,

Wpump = vf (P4 - P3) kJ/kg

Where, vf = specific volume of saturated liquid at state 3 (approx) in m^3/kg

P4 and P3 are pressure values at specific states in kPa. We get pump work in the units kJ/kg.

Once, we find out the pump work using the above formula. We calculate H4 using the relation,

H4 = H3+ Wp kJ/kg

What is the effect of increasing boiler pressure on pump work?

If the boiler pressure is increased (High pressure line moved up). Pressure at state point P4 increases. Hence,

The pump work increases

Net work output decreases

The pump work can be simply calculated by using the formula Wpump = Hout - Hin

which is Wp = H4 - H3 in the following case. The enthalpy at the pump inlet can be easily found using the steam tables, which is nothing but saturated liquid enthalpy on the low-pressure line. The problem is it is not easy to calculate the enthalpy at the exit of the pump H4 as it is in the compressed liquid region.

So, we can not directly use Wp = H4 - H3 formula to calculate pump work as we don't know H4 yet.

Hence, here we use one of the four core thermodynamic relations (called Gibbs relations)

dh = Tds+vdp

In the Rankine cycle, the pump is assumed to be isentropic hence the term Tds vanishes. We remain with the equation

dh = vdp.

When above equation is integrated between states 3 and 4, the pump work can be derived as,

Wpump = vf (P4 - P3)kJ/kgWhere, vf = specific volume of saturated liquid at state 3 (approx) in m^3/kg

P4 and P3 are pressure values at specific states in kPa. We get pump work in the units kJ/kg.

Once, we find out the pump work using above formula. We calculate H4 using the relation,

H4 = H3+ WpkJ/kgWhat is the effect of increasing boiler pressure on pump work?If the bolier pressure is increased (High pressure line moved up). Pressure at state point P4 increases. Hence,

The pump work increases

Net work output decreases