Question

Find the absolute value of specific work input required my pumps 3 and 4 in J/kg

warm moist air D Pump3 Coo water Spray condenser 'Gate valves AZBE ool condenser water B COOL Waar besim AZAB cooling tower А Pump4 River Check valve & strainer

I will include all the data I have as I'm not sure what is relevant to determine this.

Pump1 at the reactor zone electrical power consumption: P_pump1 = 21 kW

Pump2 between condenser and steam generator electrical power consumption: P_pump2 = 781.1 kW

Power output from turbine: W_T = 46,642.2 kW

Pressure drop across the condenser for the cooling water:    Δp_CD = 24.1 kPa

Temperature rise in the condenser for the cooling water: ΔT_CD = 13.5 ^oC

River water temperature: 6.5^oC

The cool water basin temperature:     15.5 ^oC

Electric efficiency of the generator: η_electric= 90.6 %

Cooling water pipe length for stage AB 45.1 m

Cooling water pipe length for stage BC 15.35 m

Cooling water pipe length for stage DE 15.35 m

Elevation difference between AB ΔZ_AB= 18.2 m

Elevation difference between BE ΔZ_BE=  5.6 m

Velocity at the surface of the cool water basin: C_B = 0 m/s

Velocity at the exit of the warm water spray: Same as velocity in the pipe

Pump3 & Pump4 have an efficiency of:    η_pump = 63 %

diameter of pipeline 0.472m

The specific enthalpy at the entry of the turbine = 2879.6 kJ/kg

   The specific enthalpy at the exit of the turbine = 1918.5 kJ/kg

   The specific enthalpy at the exit of the condenser = 242 kJ/kg

2.A. the mass flow rate of the steam in the secondary loop:     ____48.53________ kg/s

2.B. the mass flow rate of the cooling water in the tertiary loop:   _______1441.07_____ kg/s

  For the pipe section AB:

. the mean velocity of the water:   ______8.24______ m/s

.

. the Reynold's number:     _____3067842.1_______

. The type of flow:   

. The friction factor: _0.00369________ ​                                                                  

For the pipe section BE:

the mean velocity of the water:   _____8.255_______ ​​m/s

  the Reynold's number:    ___4084976.7_________ ​

The friction factor: _0.00367________ ​                                                                  

Answer 1

We are asked to find:

• the absolute value of specific work input required by pump3 in J/kg
• the absolute value of specific work input required by pump4 in J/kg

The pump 3 is used to:

• overcome frictional head loss (in the form of heat)
• overcome enthalpic changes

So, if we consider an open system with inlet occuring at B and exit occuring at E, and the entire pipe from BC through CD and DE as the control volume, then applying SFEE:

where

• c = specific heat of water = 4.187 kJ/kgK
• T1 = cool water basin temperature = 15.5 C
• V1 = Velocity at cool water basin = 0 m/s
• g = 9.81 m/s2
• z1 = height of B = 0 (considered datum)
• Q = heat gained by the cooling water in condenser =
  • c = 4.187 kJ/kgK
  • = temp rise in the condenser of the cooling water = 13.5 C
• Q(friction) = heat lost due to frictional head loss = ?
• W(pump-3) = work done by the pump on the system = ?
• T2 = T1 + T(cond) = 15.5 + 13.5 = 29 C
• V2 = average water velocity in pipe system BE = 8.255 m/s (given)
• Z2 = Z1 + Z(BE) = 0 + 5.6 = 5.6 m

Total head loss = Head loss in the pipes due to friction + Pressure head loss in the condenser

Head loss in the pipes due to friction =

where

• f = friction factor = 0.00368
• L = total length from B to E = BC + DE = 15.35 + 15.35 = 30.7 m
• D = dia of pipe = 0.472 m (given)
• V(BE) = average velocity in pipe BE = 8.255 m/s
• g = 9.81 m/s2

Pressure head loss in the condenser =

where

• = pressure drop in the condenser = 24.1 kPa = 24100 Pa
• w = specific weight of water = 9810 N/m3

Total head loss = = H1 + H2 = 0.8313 + 2.457 = 3.2883 m

Total specific energy loss =

where

• H(total) = 3.2883 m
• w = specific weight of water = 9810 N/m3
• v = average specific volume of water at mean temperature of 22.25 C = 0.001002 m3/kg [from the steam tables]

So,

[Negative sign indicates work done by the pump]

This is the ideal work. The actual work is:

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We will do the same process for pipe section AB:

where

• c = specific heat of water = 4.187 kJ/kgK
• T1 = river temperature = 6.5 C
• V1 = Velocity at river = 0 m/s [assuming still]
• g = 9.81 m/s2
• z1 = height of A = 0 (considered datum)
• Q(friction) = heat lost due to frictional head loss = ?
• W(pump-4) = work done by the pump on the system = ?
• T2 = cool water basin temperature = 15.5 C
• V2 = average water velocity in pipe system AB = 8.24 m/s (given)
• Z2 = Z1 + Z(AB) = 0 + 18.2 = 18.2 m

Total head loss = Head loss in the pipes due to friction

Head loss in the pipes due to friction =

where

• f = friction factor = 0.00369
• L = total length = AB = 45.1 m
• D = dia of pipe = 0.472 m (given)
• V(AB) = average velocity in pipe AB = 8.24 m/s
• g = 9.81 m/s2

Total head loss = = H1 = 1.22 m

Total specific energy loss =

where

• H(total) = 1.22 m
• w = specific weight of water = 9810 N/m3
• v = average specific volume of water at mean temperature of 11 C = 0.001 m3/kg [from the steam tables]

So,

[Negative sign indicates work done by the pump]

This is the ideal work. The actual work is:

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The work done by the pump 4 IS MUCH GREATER THAN the work done by pump 3. This is because, if we were to neglect the potential energy heads, the temperature of water is rising quite considerably, from 6.5 C (in the pond) to 15.5 C (in the cooling tower). This causes the work input to increase a lot, because water has a very high specific heat.

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