ucgy ior potn electic and gas burners. raon 3-62 The water in a large lake is to

Question

ucgy ior potn electic and gas burners. raon 3-62 The water in a large lake is to be used to gene -hp (shaft output) motor that has an efficiencytricity by the installation of a hydraulic turbine-generator at a nt is worn out and is to be replaced by a high- location where the depth of the water is 50 m. Water is to be tor that has an efficiency of 95.4 percent. The supplied at a rate of 5000 kg/s. If the electric power generated s 4368 hours a year at a load factor of 0.75. Taking is measured to be 1862 kW and the generator efficiency ctricity to be S0.12k Wh, determine the amount 95 percent, determine (a) the overall efficiency of the turbine money saved as a result of installing the high- generator, (b) the mechanical efficiency of the turbine, and operatin r instead of the standard motor. Also, determine ack period if the purchase prices of the standard ncy motors are $5449 and $5520, respectively (c) the shaft power supplied by the turbine to the generator 3-63 3-70 W reservoir free surfa the lower be 0.03 r to therma A 7-hp (shaft) pump is used to ra se water to an ele ation of 15 m. If the mechanical efficiency of the pump 2 percent, determine the maximum volume flow rate of water r an electric motor with a shaft power fficiency of 88 percent. Determine the rate at 3-64 At a certain location, wind is blowing steadily dissipates heat to the room it is in when the 7 m/s. Determine the mechanical energy of air per unit mass t full load. In winter, this room is normally and the power generation potential of a wind turbine with W resistance heater. Determine if it is neces80-m-diameter blades at that location. Also determine the eater on when the motor runs at full load actual electric power generation assuming an overall effi n requirements of a manufacturing facility are ciency of 30 percent. Take the air density to be 1.25 kg/m ler whose rated heat input is 5.5 x 10° Btu/h. 3-65 Reconsider Prob. 3-64. Using an appropriate ficiency of the boiler is measured to be ld flue gas analyzer. After tuning up the and the blade span diameter on wind power generation. ion efficiency rises to 0.8. The boiler oper Let the velocity vary from 5 to 20 m/s in increments of 5 m/s, year intermittently. Taking the unit cost of and the diameter vary from 20 to 120 m in increments of 10° Btu, determine the annual energy and sult of tuning up the boiler software, investigate the effect of wind velocity 20 m. Tabulate the results, and discuss their si

Explanation / Answer

Mechanical energy = KE = 1/2 mv2

Mechanical energy per unit mass = v2/2 = 49/2 = 24.5 J/kg

Mass flow rate = Area x density x velocity

For the turbine, Area = ? d2/4 = 3.14 x 802/4 = 5026.55 m2

Thus, mass flow rate = 5026.55 x 1.25 x 7 = 43982 kg/s

Theoritical power generation = mass flow rate x Mexh energy per unit mass = 43982 kg/s x 24.5 J/kg = 1077566 J/s = 1.0776 MW

Since efficiency is 0.3,

Actual power generation = 1.0776 MW x 0.3 = 0.323 MW = 323 kW

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