Steam exiting the turbine of a steam power plant at 100°F is to be condensed in a large condenser by cooling water flowing through copper pipes (k = 223 Btu/h · ft · °F) of inner diameter 0.4 in. and outer diameter 0.6 in. at an average temperature of 70°F. The heat of vaporization of water at 100°F

Question

Steam exiting the turbine of a steam power plant at 100°F is to be condensed in a large condenser by cooling water flowing through copper pipes ([latex]k = 223 Btu / h \cdot ft \cdot{ }^{\circ} F[/latex]) of inner diameter 0.4 in. and outer diameter 0.6 in. at an average temperature of 70°F. The heat of vaporization of water at 100°F is [latex]1037 Btu / lbm[/latex]. The heat transfer coefficients are [latex] 1500 Btu / h \cdot ft ^{2} \cdot{ }^{\circ} F[/latex] on the steam side and [latex]35 Btu / h \cdot ft ^{2} \cdot{ }^{\circ} F[/latex] on the water side. Determine the length of the tube required to condense steam at a rate of [latex]120 lbm / h[/latex].

Accepted Answer

Steam exiting the turbine of a steam power plant at 100°F is to be condensed in a large condenser by cooling water flowing through copper tubes. For specified heat transfer coefficients, the length of the tube required to condense steam at a rate of 400 lbm/h is to be determined.

Assumptions 1 Heat transfer is steady since there is no indication of any change with time. 2 Heat transfer is one-dimensional since there is thermal symmetry about the center line and no variation in the axial direction. 3 Thermal properties are constant. 4 Heat transfer coefficients are constant and uniform over the surfaces.

Properties The thermal conductivity of copper tube is given to be [latex] k=223 Btu / h \cdot ft \cdot{ }^{\circ} F[/latex]. The heat of vaporization of water at 100°F is given to be 1037 Btu/lbm.

Analysis The individual resistances are

[latex] A_{i}=\pi D_{i} L=\pi(0.4 / 12 ft )(1 ft )=0.105 ft ^{2}[/latex]

[latex] A_{o}=\pi D_{o} L=\pi(0.6 / 12 ft )(1 ft )=0.157 ft ^{2}[/latex]

[latex] R_{i}=\frac{1}{h_{i} A_{i}}=\frac{1}{\left(35 Btu / h \cdot ft ^{2} \cdot{ }^{\circ} F ight)\left(0.105 ft ^{2} ight)}=0.27211 h \cdot ^{\circ} F / Btu [/latex]

[latex] R_{ ext {pipe }}=\frac{\ln \left(r_{2} / r_{1} ight)}{2 \pi k L}=\frac{\ln (3 / 2)}{2 \pi\left(223 Btu / h \cdot ft \cdot{ }^{\circ} F ight)(1 ft )}=0.00029 h \cdot ^{\circ} F / Btu[/latex]

[latex] R_{o}=\frac{1}{h_{o} A_{o}}=\frac{1}{\left(1500 Btu / h \cdot ft ^{2} \cdot{ }^{\circ} F ight)\left(0.157 ft ^{2} ight)}=0.00425 h \cdot ^{\circ} F / Btu [/latex]

[latex] R_{ ext {total }}=R_{i}+R_{ ext {pipe }}+R_{o}=0.27211+0.00029+0.00425=0.27665 h \cdot ^{\circ} F / Btu[/latex]

The heat transfer rate per ft length of the tube is

[latex] \dot{Q}=\frac{T_{\infty 1}-T_{\infty 2}}{R_{ ext {total }}}=\frac{(100-70)^{\circ} F }{0.27665^{\circ} F / Btu }=108.44 Btu / h [/latex]

The total rate of heat transfer required to condense steam at a rate of 400 lbm/h and the length of the tube required is determined to be

[latex] \dot{Q}_{ ext {total }}=\dot{m} h_{f g}=(120 lbm / h )(1037 Btu / lbm )=124,440 Btu / h [/latex]

[latex] ext { Tube length }=\frac{\dot{Q}_{ ext {total }}}{\dot{Q}}=\frac{124,440}{108.44}=1148 ft [/latex]

Question 3.78.E: Steam exiting the turbine of a steam power plant at 100°F is...

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