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Material and energy

Fluid-flow theory
Fluid-flow applications
Heat-transfer theory

separation processes


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1. Material and energy balances can be worked out quantitatively knowing the amounts of materials entering into a process, and the nature of the process.

2. Material and energy balances take the basic form
Content of inputs = content of products + wastes/losses + changes in stored materials.

3. In continuous processes, a time balance must be established.

4. Energy includes heat energy (enthalpy), potential energy (energy of pressure or position), kinetic energy, work energy, chemical energy.
It is the sum over all of these that is conserved.

5. Enthalpy balances, considering only heat, are useful in many food processing situations.


1. If 5 kg of sucrose are dissolved in 20 kg of water estimate the concentration of the solution in (a) w/w, (b) w/v, (c) mole fraction, (d) molar concentration.
The density of a 20% sucrose solution is 1070 kg m-3, molecular weight of sucrose 342

(a) 20%, (b) 21.4% (c) 0.018 (d) 0.63 mol m-3

2. If 1 m3 of air at a pressure of 1 atm is mixed with 0.1 m3 of carbon dioxide at 1.5 atm and the mixture is compressed so that its total volume is 1 m3, estimate the concentration of the carbon dioxide in the mixture in (a) w/w, (b) w/v, (c) mole fraction at a temperature of 25°C. Mean molecular weight of air is 28.8, and of carbon dioxide 44. (a) 18.6%, (b) 27%, (c) 0.13

3. It is convenient to add salt to butter, produced in a continuous buttermaking machine, by adding a slurry of salt with water containing 60% of salt and 40% of water by weight. If the final composition of the butter is to be 15.8% moisture and 1.4% salt, estimate the original moisture content of the butter prior to salting.(15.2%)

4. In a flour mill, wheat is to be adjusted to a moisture content of 15% on a dry basis. If the whole grain received at the mill is found to contain 11.4% of water initially, how much water must the miller add per 100 kg of input grain as received, to produce the desired moisture content? (1.8 kg/ 100 kg)

5. (a) In an analysis, sugar beet is found to contain 75% of water and 17.5% of sugar. Of the remaining material, 25% is soluble and 75% insoluble, calculate the sugar content of the expressible juice assumed to contain water and all soluble solids pro rata.
(b) If the beets are extracted by addition of a weight of water equal to their own weight and after a suitable period the soluble constituents are concentrated evenly throughout all the water present, calculate the percentage of the total sugar left in the drained beet and the percentage of the total sugar extracted, assuming that the beet cells (insoluble) after the extraction have the same quantity of water associated with them as they did in the original beet.

(c) Lay out a mass balance for the extraction process
(a) 18.5% (b) drained beet 43%, extract 57%

6. A sweet whey, following cheesemaking, has the following composition: 5.5% lactose, 0.8% protein. 0.5% ash. The equilibrium solubility of lactose in water is:
Temp. °C
  Lactose solubility kg/l00 kg water

Calculate the percentage yield of lactose when 1000 kg of whey is concentrated in a vacuum evaporator at 60°C to 60% solids and the concentrate is then cooled with crystallization of the lactose, down to 20°C over a period of weeks.

7. In an ultrafiltration plant, whey is to be concentrated. Two streams are to be produced, a protein rich stream and a liquid (mainly water) stream.In all 140,000 kg per day are to be processed to provide a 12-fold concentration of 95% of the protein from an original whey concentration of 0.93% protein and 6% of other soluble solids.
Assuming that all of the soluble solids other than protein remain with the liquid stream, which also has the 5% of the protein in it, estimate the daily flows and concentrations of the two product streams.
((a) protein stream: 11,084 kg day-1,11.16% protein,(b) liquid stream 128,916 kgday-1, 0,05% protein)

8. It is desired to prepare a sweetened concentrated orange juice. The initial pressed juice contains 5 % of total solids and it is desired to lift this to 10% of total solids by evaporation and then to add sugar to give 2% of added sugar in the concentrated juice. Calculate the quantity of water which must be removed, and of sugar which must be added with respect to each 1000 kg of pressed juice.
(water removed 500 kg,sugar added 10.2 kg)

9. A tomato-juice evaporator takes in juice at the rate of 1200 kg h-1. If the concentrated juice contains 35% of solids and the hourly rate of removal of water is 960 kg, calculate the moisture content of the original juice and the quantity of steam needed per hour for heating if the evaporator works at a pressure of 10 kPa and the heat available from the steam is 2200 kJ kg-1. Assume no heat losses.
((a) water content of juice, 93%, (b) steam needed 1089 kg h-1))

10. Processing water is to be heated in a direct fired heater, which burns natural gas with a calorific value of 20.2 MJ m-3. If 5000 kg h-1 of this water has to be heated from 15°C to 80°C and the heater is estimated to be 45% efficient, estimate the hourly consumption of gas.
150 m3.

Figure 2.3 Casein Process
Figure 2.3 Casein process

11. In a casein factory (see Fig. 2.3) the entering coagulum containing casein and lactose is passed through two cookers and acidified to precipitate the casein. The casein separates as a curd. The curd is removed pressed from the whey by screening, and then washed, and dried. The casein fines are removed from the raw whey from screening and the wash water by hydrocyclones, and mixed with the heated coagulum just before screening. The cycloned whey is used for heating in the first cooker and steam in the second cooker by indirect heating. The casein and lactose contents of the various streams were determined.

% Composition
on Wet Weight Basis
Raw whey from screening
Whey (cycloned)
Wash water
Waste wash water
Dried product

From these data calculate complete mass balances for the process, using a simple step-by-step approach, starting with the hydrocyclones. Assume lactose completely soluble in all solutions. and concentrations in fines and wastes streams from hydrocyclones are the same.

(a) Set out an overall mass balance for the complete process to the production of the wet curd. i.e. until. after the washing/pressing operation. Start the mass balance at the hydrocyclones i.e. mass balances for the following unit operations: hydrocyclones, cooking, screening,washing; and then an overall balance.
(b) Set out a casein mass balance over the same unit operations, and overall. Assume that there was little or no casein removed from the whey cyclones, and lost from the coagulum.
(c) Set out a lactose balance on the screening and washing.
(d) Set out a mass balance from the wet curd to the dried product. Assume that the product contains only casein, lactose and water.
(e) What was the composition of the wet curd? (41.8% casein, 0.3% lactose, 57..9% water)
(f)  What was the composition of the final product? (87.4% casein, 0.69% lactose, 11.9% water)
(g) Determine the yield of the casein from the coagulum entering, and the losses in the cycloned whey. and waste water   (99.6%, in waste whey 0.2%, in waste water 0.2%)


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Unit Operations in Food Processing. Copyright © 1983, R. L. Earle. :: Published by NZIFST (Inc.)
NZIFST - The New Zealand Institute of Food Science & Technology