Sample Problems in Industrial Plant Design Pumps Problem No. 1 Determine the specific speed of a centrifugal pump delivering 7500 gpm acting against a total head of 370 feet and operating at 1000 rpm. Given: Q = 7500 gpm H = 370 ft N = 1000 rpm Find: Ns = ? Solution: √
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Problem No. 2 Pumps A and B belong to the same family and are operating at homologous points. For Pump A For Pump B D = 2 feet D = 3 feet N = 1000 rpm Q = 6500 gpm At its best efficiency point (BEP) H = 200 feet Q = 8000 gpm How fast should pump B run if it s to operate as its best efficiency point?
Solution: By Pumps Similarity Laws
Problem No. 3 A centrifugal pump is used to deliver 500 000 li/hr of water from a reservoir located 5 meters below the pump to a pressure tank whose pressure is 3 kg/cm 2. It is also estimated that friction losses in the 250-mm suction and 175-mm discharge pipe are 3 m and 1.5 m, respectively. Assuming a pup efficiency of 68%, calculate for the nominal rating of the motor in kW. Given: Q = 500 000 li/hr H=5m P2 = 3 kg/cm2 = 294.1995 KPa Ds = 250 mm hfs = 3 m Dd = 175 mm hfd = 1.5 m ηpump = 68% Find: Pbrake = ? Solution: (
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Problem No. 4 A mixed-flow pump operating at 500 rpm and delivering 60m3/min has a specific speed of 100 rpm. The suction flange is 600 mm in diameter and has an absolute pressure of 50 kPA. The discharge flange is 520 mm in diameter and its centerline is 40cm above the suction centerline. Account for the expected discharged pressure.
Solution: √
Where:
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Where:
Problem No. 5 A boiler feed pump receives 300 liters of water at 90◦C (h = 839.33 kJ/kg) per minute. It is operating against a total head of 800 m. calculate for the enthalpy of the fluid leaving the pump, in kJ/kg. Assume a pump efficiency of 70 per cent. Solution:
Compressor Problem No. 1 A rotary compressor takes in 360 kg/hr of air at 1 bar, 20°C and compresses it to 600 kPa with an isentropic compressor efficiency of 75 per cent. Find the power required to drive the compressor in kW. Given: m = 360kg/hr P1 = 1 bar = 100KPa T1 = 20oC = 293K P2 = 600 KPa n = 1.4 ηcompressor = 75% Find: Pbrake = ? Solution: [( )
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Problem No. 2 An air compressor with a clearance of 7% handles 0.6 kg/s of air between the pressures of 1 atm and 400 kPa with a poly tropic constant of 1.25. Temperature of the air at the beginning of compression is 27°C. Calculate for the transferred heat during the compression process, in kW.
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Problem No. 3 A two stage reciprocating air compressor is required to deliver 0.9 kg/s of air from 1 bar and 27°C to 10 bars. The compressor operates at 300 rpm, compression and expansion processes follow Pv1.33 = constant, and both cylinders have 4.25 per cent clearance. There is a 10-kPa pressure drop in the intercooler. The low-pressure cylinder discharges at the optimum pressure into the intercooler. Air enters the high-pressure cylinder at 30°C. Intercooler is water-cooled, with the water entering at 290 K and leaving at 300 K. Assuming a 100% heat transfer efficiency, determine the amount of cooling water required by the intercooler, in li/min.
Given: m = 0.9 kg/s P1 = 1 bar T1 = 27 oC P2 = 10 bar n = 1.33 c = 0.0425 Find: Vwater = ? Solution: √ √ ( )
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Problem No. 4 A compressor receives air from the surroundings at 1 bar, 27◦C. there is a pressure drop of 3 kPa through the intake valves and the temperature at the end of the stroke is 39◦C. discharge pressure drop through the discharge valves. Compressor capacity is 12 liters and piston displacement of 15 liters with compressor speed of 200 rpm. Assuming a poly tropic constant of 1.25, account for the probable volumetric efficiency.
Given: P1 = 1 bar = 100 KPa T1 = 27oC = 300 K P2 = 97 KPa T2 = 39oC = 312 K VC = 12 L VD = 15 L N = 200 rpm n = 1.25 Find: Ev = ? Solution: ( )
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Problem No. 5 A single acting air compressor operated at 375 rpm with an initial condition of 98 kPa 21°C and discharges the air at 400 kPa. Bore and stroke are 350 mm and 400 mm, respectively. Determine the free air capacity in m3/s/ assume 5% clearance and poly tropic exponent of 1.25. Given: N = 375 rpm = 6.25 rev/sec P1 = 98 KPa T1 = 21oC P2 = 400 KPa D = 350 mm L = 400 mm c = 0.05 n = 1.25
Find: Free air capacity, Vair Solution:
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Machine Foundation Problem No. 1 Given the following data: 10 in x 12 in engine area 4 100-kg engine SABP of location = 6000 kg/m3 Bedplate dimensions = 5 cm x 2.5 m Design limit for foundation depth = 0.8 m Requirement: Design a rectangular block foundation that is safe against direct settlement. Express your answer in terms of L x W x H.
Solution: Allowing 1 foot (0.3m) clearance each side L = 5m + 2(0.3m) = 5.6m W = 2.5m + 2(0.3m) = 3.1m Since the design limit for foundation depth = 0.8m Therefore: L = 5.6 m; W = 3.1 m; H = 0.8 m
Problem No. 2 Determine the amount of sand in m3 required for a 5 m3 of 1:2:4 concrete mixture (refer to Construction Estimate by Max Fajardo), given the following properties:
Material
Relative Density
Cement Sand Gravel
3.50 2.75 2.25
Density, kg per m3 1300 1700 1500
As per recommendation, use 25 liters of water per bag of cement. Assume one bag of cement contains 0.03 m3 Solution: Vc, Vs, Vg, Vw = compact volume of cement, sand, sand gravel and water respectively (
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Heat Exchanger Problem No. 1 One side of a plane wall is maintained at 100°C, while the other side is exposed to a convection environment having T = 10°C and h = 10 W/m2 - °C. The wall has a thermal conductivity k = 1.6 W/m2 - °C and is 40 cm thick. Calculate for the heat flux through the wall in W/m2. Given: T1 = 100oC T2 = 10oC h1 = 10 W/m2-oC x = 40 cm = 0.4 m k = 1.6 W/m-oC Find: Q/A = ? Solution:
Problem No. 2 Hot water enters a counter flow heat exchanger at 99°C. it is used to heat a cold steam of water from 4 to 32 °C. The flow rate of the cold stream is 1.3 kg/s, and the flow rate of the hot stream is 2.6 kg/s. the overall heat transfer coefficient is 830 W/m 2 - °C. Compute for the heat exchange area in m2. Given: Hot water Th1 = 99oC mh = 2.6 kg/s U = 830 W/m2-oC Find: A=? Solution:
Cold water Tc1 = 4oC mc = 1.3 kg/s
Problem No. 3 A two-meter steel pipe with a 5-cm outer diameter is covered with a 6.4-mm layer of asbestos insulation, k = 0.096Btu/hr-ft-oF, followed by a 2.5-cm layer of fiberglass insulation, k = 0.028 Btu/hr-ft-oF. The pipe wall temperature is 315oC and the outside insulation temperature is 38oC. Determine the heat transfer in watts.
Solution:
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Transformer Problem No. 1 The secondary of a 20 Kva, 60-cycle transformer has 120 turns and the flux in the core has a maximum value of 720,000 maxwells. If the primary has 1200 turns, determine the primary voltage in volts. Given: f = 60cycle N1 = 1200 turns N2 = 120 turns Find: Primary voltage, E1 Solution:
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Refrigeration Problem No. 1 A single stage vapor-compression refrigeration system uses Freon-12 to produce 10 tons of refrigeration when operating between a condensing temperature of 40°C (960.7 KPa) and an evaporating temperature of -10°C (219.1 KPa). The specific enthalpy of saturated liquid at condenser pressure is 74.527 kJ/kg. The specific enthalpy and specific volume of saturated vapor at evaporator pressure are 183.058kj/kg, and 0.076646 /kg, respectively. Assuming the specific enthalpy of superheated vapor leaving the compressor equal to 209.5 kJ/kg.
a) b) c) d) e) f) g) h) i) j)
Determine the following: Compression ratio Refrigerating effect, in kJ/kg Refrigerant mass flow rate, in kg/s Refrigerant volume flow rate, in 3 Heat rejected in the condenser, kW Compressor power, kW COP of the system Refrigerating efficiency, Degrees superheat, °SH Compressor power, in kW, if adiabatic efficiency is 80%
Given: QA = 10 TOR T3 = 40°C P2 = P3 = T4 = 960.7 KPa P4 = 219.1 KPa h4 =h3 = 74.527 kJ/kg h1 = 183.058 kJ/kg v1 = 0.076646 h2 = 209.5 kJ/kg
/kg
Solution:
1.2
RE = h1 - h4 = (183.058 - 74.527) kJ/kg RE = 108.531 kJ/kg
1.3
m= m= m = 0.324 kg/s
1.4
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= vm
v = (0.324 kg/s) (0.076646
/kg)
v = 0.025 1.5
Wc = m (h2 - h1) Wc = (0.324 kg/s) (209.5-183.058) kJ/kg Wc = 8.57 KW
1.6
QR = m (h2 – h3) QR = (0.324 kg/s) (209.5-74.527) kJ/kg QR = 43.73 KW
1.7
COP = COP = COP = 4.10
1.0
Compressor Power =
=
= 10.71 KW
Problem No. 2 A small cold storage plant is used to store 2 metric tons of onions daily. The onions are available at 37°C and the storage temperature is -5°C. The specific heats of onions before and after freezing are 3.81kJ/kg-°C and 2.13kJ/kg-°C, respectively. The freezing temperature is -1.0°C. Latent heat of fusion is 302kJ/kg. Heat of respiration is 4 650 kJ/metric ton per 24hours. If the refrigerating machine operates 24 hours a day and the chilling rate factor is 0.80, determine the capacity of the machine required in tons of refrigeration (TR). Given: monion =2Mt = 2000kg Tonion = 37oC Tstorage = -5oC Conion = 3.81kJ/kg-oC (before freezing) = 2.13 kJ/kg-oC (after freezing) Tfreezer = -1.0oC QL = 302kJ/kg QR = 4650 kJ/Mt per 24 hour Find: Capacity of machine in TOR = ? Solution:
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Problem No. 3 An ice plant produces 20 tons of ice per day at -15 °C from water at 25°C. if miscellaneous losses are 12 per cent of the chilling and freezing load, calculate for the refrigeration capacity of the ice plant, in TR. Solution:
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Air Conditioning Problem No. 1 Indoor design conditions of a certain theatre require that 26°C dry bulb and 50% relative humidity is maintained. Air is to be supplied at 16°C where as outside air is at 30°C dry bulb and 60% relative humidity. Take the sensible heat load and latent heat load as 200 KW and 50 KW, respectively. Assuming ventilating air as 20% of the supply air, determine the tons of refrigeration required by the conditioner.
Solution:
From psychrometric chart
By mass balance:
Where:
By heat balance:
Problem No. 2 A cooling tower of a large industrial cold storage plant cools 12,000 kg/s of water from 35°C to 25°C. The inlet air to the cooling tower has a temperature of 25°C drybulb and 35% relative humidity. Air leaves the cooling tower saturated at 35°C. Calculate for the volume flow rate of air required by the cooling tower in /min if the specific volume of the inlet air is 0.75 /kg. Solution:
From psychrometric chart:
Problem No. 3 Condenser cooling water is supplied to the forced-draft fan at 40°C. The cooling tower approach temperature is 3°C. Air enters the tower at 25°C dry-bulb and 20°C wet-bulb with moisture content of 0.0128 kgv/kgda and specific enthalpy of 57.5 KJ/kgda and leaves at 38°C dry-bulb, 60% relative humidity with moisture content of 0.0256 kgv/kgda and specific enthalpy of 104 Kj/kgda. For 5 000 liters per minute of condenser water entering the cooling tower, determine the amount of make-up water requires in L/min to compensate for the evaporation losses. Solution:
Problem No. 4 A copra-drying plant is designed to dry 1000 kg/hr of fresh coconut 30% water. The raw copra from the dryer contains 5 % water. Fresh air at 27°C and 40% relative humidity and barometric pressure of 98 kPa has a humidity ratio of 0.0083 kg w/kgda and an enthalpy of 50.86Kj/kgda. The air is heated to 110°C (h=135.58kJ/kgda) before entering the adiabatic drying chamber ratio of 0.02285kgw/kgda. Assuming 100 percent heat transfer efficiency in the air preheater, find the amount of steam required by the dryer when condensing saturated steam required by the dryer when condensing saturated steam to saturated liquid at 150kPa (hfg=2226.5kJ/kg). Express answer in kg/hr. Solution:
Problem No. 5 Wet feed containing 70% moisture leaves a rotary dryer with a bone with a bone dry weight of 90%. Determine weight of moisture removed in kg based on: a) One kilogram of original wet feed b) One kilogram of final dried product c) One kilogram of bone-dry material
Solution:
a. 1kg of original wet feed
b. 1kg of dried product
c. 1 kg of bone-dry product
Bataan Peninsula State University (Main Campus) Balanga City, Bataan College of Engineering and Architecture Department of Mechanical Engineering
MEID 512 INDUSTRIAL PLANT DESIGN
Sample Problems in Industrial Plant Design
Submitted By: Surname
Given Name
Middle Initial
Cruz
Arturo
C.
Datuin
Raynierson
P.
Jayme
Jerald
F.
Matorgo
Mhar Ann Kurl
A.
Sapuyot
Kevin
C.
Tolentino
Melvin
M.
Submitted to: Engr. Alfredo D. Valentos, PME Date of Submission: October 11, 2011
