Steam exiting the turbine of a steam power plant at 100^∘ F is to be condensed in a large conden

step 1 This problem, we have another reheat ranking cycle. Again, ideal. We have a little different con

Steam exiting the turbine of a steam power plant at 100^∘ F...

Steam exiting the turbine of a steam power plant at $100^{\circ} \mathrm{F}$ is to be condensed in a large condenser by cooling water flowing through copper pipes $\left(k=223 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft}-{ }^{\circ} \mathrm{F}\right)$ of inner diameter $0.4 \mathrm{in}$ and outer diameter $0.6$ in at an average temperature of $70^{\circ} \mathrm{F}$. The heat of vaporization of water at $100^{\circ} \mathrm{F}$ is $1037 \mathrm{Btu} / \mathrm{lbm}$. The heat transfer coefficients are $2400 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft}^{2} \cdot \mathrm{F}^{\circ}$ on the steam side and $35 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft}^{2} \cdot \mathrm{F}^{\circ}$ on the water side. Determine the length of the tube required to condense steam at a rate of $250 \mathrm{lbm} / \mathrm{h}$.

Key Concepts

Energy Balance in Heat Exchangers

This concept involves equating the rate of energy removal or addition in a system to the product of the mass flow rate and the specific enthalpy change (including latent heat during phase change). It is fundamental for determining the total heat load, such as the energy released when steam condenses.

Latent Heat of Vaporization

Latent heat of vaporization is the amount of energy released or absorbed during the phase change of a substance at constant temperature. In condenser applications, the steam releases its latent heat as it condenses, which drives the heat transfer process.

Thermal Resistance Network

This concept refers to analyzing the combined resistances to heat transfer that occur in series, such as convection from the steam to the tube surface, conduction through the tube wall, and convection from the tube to the cooling water. Summing these resistances yields the overall thermal resistance of the system.

Overall Heat Transfer Coefficient

The overall heat transfer coefficient consolidates the effects of various heat transfer resistances into a single parameter, allowing the design and analysis of heat exchangers. It is used to relate the heat transfer rate to the effective driving temperature difference and the surface area available for heat transfer.

Logarithmic Mean Temperature Difference (LMTD)

The LMTD is an averaging method used in heat exchanger calculations to account for the changing temperature difference between two fluids over the length of the exchanger. It provides an effective mean temperature difference which is essential for accurately determining the required heat transfer area.

Transcript

00:01 This problem, we have another reheat ranking cycle.

00:08 Again, ideal.

00:10 We have a little different condition here.

00:12 This time, coming out of the high -pressure turbine, we have saturated vapor, and then that's reheated.

00:26 And then we have, we're basically in the two -phase region here coming out of the low -pressure.

00:32 Pressure turbine.

00:35 So again, i should probably, like i said before, make this a black line.

00:42 So we have, you know, all these entropies are the same because we have ideal cases for the turbines and for the pump.

00:51 The high pressure, we're in english units now, the high pressure side is at 800 psia.

00:59 Again, we have a quality factor of one at four.

01:04 Let's see here.

01:05 We also have, let's see, heat is transferred.

01:13 We have, so we have steam as cooled in the gantar by cooling water from a nearby river.

01:19 So the river temperature is, what do you call it, is 45 degrees fahrenheit.

01:32 So that enters the condenser here.

01:36 And so we basically have a heat exchanger here to condense this vapor.

01:44 Up here we have 900 degrees fahrenheit and down here we have one psia so very low pressure down here and the condenser.

01:59 Let's see here now t1, again we are at saturated liquid here so t1 is roughly 101 .7 degrees because we're at a very low pressure here.

02:18 Let's see here.

02:21 Anyway, yeah, that's kind of a, oh yeah, no, no, yeah.

02:25 I'm thinking celsius.

02:26 Like, why is that over 100 celsius? no, it's fahrenheit.

02:29 So that's why it's below 212.

02:32 So 212 fahrenheit is where water boils.

02:35 So yeah, why we're way below is because we're at very low pressure.

02:39 Now we can figure out the enthalpy there, and that is, um, 69 .72 btu per pound mass and we can figure out the specific volume, which then allows us to figure out the work that is being done put into the pump with the specific work, which then allows us to find the enthalpy at 2, as always.

03:12 Then we can look at 0 .3 here.

03:14 We have the pressure and the temperature, so we can get the entropy and the entropy.

03:19 Entropy at 4 is the same as entropy at 3.

03:23 So we can figure out the pressure at 4, which is actually pretty low.

03:29 We drop down a lot in pressure.

03:34 And then we can also get the enthalpy at 4.

03:38 We can find the enthalpy at 5 because we have the, let's see here, the temperature at 5.

03:51 And we know the pressure at 5, because this is also, i should just write that in here.

04:01 P5 equals p4.

04:05 So we know the pressure and temperature at 5, so we can get the enthalpy and the entropy...

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