Safari Books Online is a digital library providing ondemand subscription access to thousands of learning resources.
8.41. 
HeatTransfer Coefficient in SingleEffect Evaporator. A feed of 4535 kg/h of a 2.0 wt % salt solution at 311 K enters continuously a singleeffect evaporator and is being concentrated to 3.0%. The evaporation is at atmospheric pressure and the area of the evaporator is 69.7 m^{2}. Saturated steam at 383.2 K is supplied for heating. Since the solution is dilute, it can be assumed to have the same boiling point as water. The heat capacity of the feed can be taken as c_{p} = 4.10 kJ/kg · K. Calculate the amounts of vapor and liquid product and the overall heattransfer coefficient U. 
A1:  Ans. U = 1823 W/m^{2} · K 
8.42. 
Effects of Increased Feed Rate in Evaporator. Using the same area, value of U, steam pressure, evaporator pressure, and feed temperature as in Problem 8.41, calculate the amounts of liquid and vapor leaving and the liquid outlet concentration if the feed rate is increased to 6804 kg/h. 
A2:  Ans. V = 1256 kg/h, L = 5548 kg/h, x_{L} = 2.45% 
8.43. 
Effect of Evaporator Pressure on Capacity and Product Composition. Recalculate Example 8.41 but use an evaporator pressure of 41.4 kPa instead of 101.32 kPa abs. Use the same steam pressure, area A, and heattransfer coefficient U in the calculations.

8.44. 
Production of Distilled Water. An evaporator having an area of 83.6 m^{2} and U = 2270 W/m^{2} · K is used to produce distilled water for a boiler feed. Tap water having 400 ppm dissolved solids at 15.6°C is fed to the evaporator operating at 1 atm pressure abs. Saturated steam at 115.6°C is available for use. Calculate the amount of distilled water produced per hour if the outlet liquid contains 800 ppm solids. 
8.45. 
BoilingPoint Rise of NaOH Solutions. Determine the boiling temperature of the solution and the boilingpoint rise for the following cases:

A5:  Ans. (a) Boiling point = 130.6°C, boilingpoint rise = 15°C 
8.46. 
BoilingPoint Rise of Biological Solutes in Solution. Determine the boilingpoint rise for the following solutions of biological solutes in water. Use the figure in (P1), pp. 11112.

A6:  Ans. (a) Boilingpoint rise = 2.2°F (1.22°C) 
8.47. 
Effect of Feed Temperature on Evaporating an NaOH Solution. A singleeffect evaporator is concentrating a feed of 9072 kg/h of a 10 wt % solution of NaOH in water to a product of 50% solids. The pressure of the saturated steam used is 42 kPa (gage) and the pressure in the vapor space of the evaporator is 20 kPa (abs). The overall heattransfer coefficient is 1988 W/m^{2} · K. Calculate the steam used, the steam economy in kg vaporized/kg steam, and the area for the following feed conditions:

A7:  Ans. (a) S = 8959 kg/h of steam, A = 296.9 m^{2} 
8.48. 
HeatTransfer Coefficient to Evaporate NaOH. In order to concentrate 4536 kg/h of an NaOH solution containing 10 wt % NaOH to a 20 wt % solution, a singleeffect evaporator is being used, with an area of 37.6 m^{2}. The feed enters at 21.1°C (294.3 K). Saturated steam at 110°C (383.2 K) is used for heating and the pressure in the vapor space of the evaporator is 51.7 kPa. Calculate the kg/h of steam used and the overall heattransfer coefficient. 
8.49. 
Throughput of a SingleEffect Evaporator. An evaporator is concentrating F kg/h at 311 K of a 20 wt % solution of NaOH to 50%. The saturated steam used for heating is at 399.3 K. The pressure in the vapor space of the evaporator is 13.3 kPa abs. The overall coefficient is 1420 W/m^{2} · K and the area is 86.4 m^{2}. Calculate the feed rate F of the evaporator. 
A9:  Ans. F = 9072 kg/h 
8.410. 
Surface Area and Steam Consumption of an Evaporator. A singleeffect evaporator is concentrating a feed solution of organic colloids from 5 to 50 wt %. The solution has a negligible boilingpoint elevation. The heat capacity of the feed is c_{p} = 4.06 kJ/kg · K (0.97 btu/lb_{m} · °F) and the feed enters at 15.6°C (60°F). Saturated steam at 101.32 kPa is available for heating, and the pressure in the vapor space of the evaporator is 15.3 kPa. A total of 4536 kg/h (10 000 lb_{m}/h) of water is to be evaporated. The overall heattransfer coefficient is 1988 W/m^{2} · K (350 btu/h · °F). What is the required surface area in m^{2} and the steam consumption? 
8.411. 
Evaporation of Tomato Juice Under Vacuum. Tomato juice having a concentration of 12 wt % solids is being concentrated to 25% solids in a filmtype evaporator. The maximum allowable temperature for the tomato juice is 135°F, which will be the temperature of the product. The feed enters at 100°F. Saturated steam at 25 psia is used for heating. The overall heattransfer coefficient U is 600 btu/h · ft^{2} · °F and the area A is 50 ft^{2}. The heat capacity of the feed c_{p} is estimated as 0.95 btu/lb_{m} · °F Neglect any boilingpoint rise if present. Calculate the feed rate of tomato juice to the evaporator. 
8.412. 
Concentration of Cane Sugar Solution. A singleeffect evaporator is being used to concentrate a feed of 10 000 lb_{m}/h of a cane sugar solution at 80°F and containing a sugar content of 15° Brix (degrees Brix is wt % sugar) to 30° Brix for use in a food process. Saturated steam at 240°F is available for heating. The vapor space in the evaporator will be at 1 atm abs pressure. The overall U = 350 btu/h · ft^{2} · °F and the heat capacity of the feed is c_{p} = 0.91 btu/lb_{m} · °F The boilingpoint rise can be estimated from Example 8.51. The heat of solution can be considered negligible and neglected. Calculate the area required for the evaporator and the amount of steam used per hour. 
A12:  Ans. Boilingpoint rise = 2.0°F (1.1°C), A = 667 ft^{2} (62.0 m^{2}) 
8.51. 
Boiling Points in a TripleEffect Evaporator. A solution with a negligible boilingpoint rise is being evaporated in a tripleeffect evaporator using saturated steam at 121.1°C (394.3 K). The pressure in the vapor of the last effect is 25.6 kPa abs. The heattransfer coefficients are U_{1} = 2840, U_{2} = 1988, and U_{3} = 1420 W/m^{2} · K, and the areas are equal. Estimate the boiling point in each of the evaporators. 
A13:  Ans. T_{1} = 108.6°C (381.8 K) 
8.52. 
Evaporation of Sugar Solution in a MultipleEffect Evaporator. A tripleeffect evaporator with forward feed is evaporating a sugar solution with negligible boilingpoint rise (less than 1.0 K, which will be neglected) and containing 5 wt % solids to 25% solids. Saturated steam at 205 kPa abs is being used. The pressure in the vapor space of the third effect is 13.65 kPa. The feed rate is 22 680 kg/h and the temperature 299.9 K. The liquid heat capacity is c_{p} = 4.19 – 2.35 x, where c_{p} is in kJ/kg · K and x in wt fraction (K1). The heattransfer coefficients are U_{1} = 3123, U_{2} = 1987, and U_{3} = 1136 W/m^{2} · K. Calculate the surface area of each effect if each effect has the same area, and the steam rate. 
A14:  Ans. Area A = 99.1 m^{2}, steam rate S = 8972 kg/h 
8.53. 
Evaporation in DoubleEffect ReverseFeed Evaporators. A feed containing 2 wt % dissolved organic solids in water is fed to a doubleeffect evaporator with reverse feed. The feed enters at 100°F and is concentrated to 25% solids. The boilingpoint rise can be considered negligible, as can the heat of solution. Each evaporator has a 1000ft^{2} surface area, and the heattransfer coefficients are U_{1} = 500 and U_{2} = 700 btu/h · ft^{2} · °F. The feed enters evaporator number 2 and steam at 100 psia is fed to number 1. The pressure in the vapor space of evaporator number 2 is 0.98 psia. Assume that the heat capacity of all liquid solutions is that of liquid water. Calculate the feed rate F and the product rate L_{1} of a solution containing 25% solids. (Hint: Assume a feed rate of, say, F = 1000 lb_{m}/h and a value of T_{1}. Calculate the area and T_{1}. Then calculate the actual feed rate by multiplying 1000 by 1000/calculated area.) 
A15:  Ans. F = 133 800 lb_{m}/h (60 691 kg/h), L_{1} = 10 700 lb_{m}/h (4853 kg/h) 
8.54. 
Concentration of NaOH Solution in TripleEffect Evaporator. A forcedcirculation tripleeffect evaporator using forward feed is to be used to concentrate a 10 wt % NaOH solution entering at 37.8°C to 50%. The steam used enters at 58.6 kPa gage. The absolute pressure in the vapor space of the third effect is 6.76 kPa. The feed rate is 13 608 kg/h. The heattransfer coefficients are U_{1} = 6246, U_{2} = 3407, and U_{3} = 2271 W/m^{2} · K. All effects have the same area. Calculate the surface area and steam consumption. 
A16:  Ans. A = 97.3 m^{2}, S = 5284 kg steam/h 
8.55. 
TripleEffect Evaporator with Reverse Feed. A feed rate of 20 410 kg/h of 10 wt % NaOH solution at 48.9°C is being concentrated in a tripleeffect reversefeed evaporator to produce a 50% solution. Saturated steam at 178.3°C is fed to the first evaporator and the pressure in the third effect is 10.34 kPa abs. The heattransfer coefficient for each effect is assumed to be 2840 W/m^{2} · K. Calculate the heattransfer area and the steam consumption rate. 
8.56. 
Evaporation of Sugar Solution in DoubleEffect Evaporator. A doubleeffect evaporator with reverse feed is used to concentrate 4536 kg/h of a 10 wt % sugar solution to 50%. The feed enters the second effect at 37.8°C. Saturated steam at 115.6°C enters the first effect and the vapor from this effect is used to heat the second effect. The absolute pressure in the second effect is 13.65 kPa abs. The overall coefficients are U_{1} = 2270 and U_{2} = 1705 W/m^{2} · K. The heating areas for both effects are equal. Use boilingpointrise and heatcapacity data from Example 8.51. Calculate the area and steam consumption. 
8.61. 
Water Consumption and Pressure in Barometric Condenser. The concentration of NaOH solution leaving the third effect of a tripleeffect evaporator is 50 wt %. The vapor flow rate leaving is 5670 kg/h and this vapor goes to a barometric condenser. The discharge water from the condenser leaves at 40.5°C. Assuming that the condenser can maintain a vacuum in the third effect corresponding to a saturated vapor pressure of 2.78°C above 40.5°C, calculate the pressure in the third effect and the coolingwater flow to the condenser. The cooling water enters at 29.5°C. (Note: The vapor leaving the evaporator will be superheated because of the boilingpoint rise.) 
A19:  Ans. Pressure = 8.80 kPa abs, W = 306 200 kg water/h 