Hints for 3-17a) setup the mass fractions and mass flows in a large table, adjus

Question

Hints for 3-17a) setup the mass fractions and mass flows in a large table, adjust all the alloy feed flow rates together (yes all the same) to get the target value.

Hints for 3-17b) first bullet: Setup the mass fractions and mass flows for mixer 1 as asked, insert the relationship for mass fractions for mixer 1 out based on the flow in and the unknown mass flow rates. Include a calculation of the sum of mass fractions for mixer 1 and sum of mass flows. You end up with two unknowns, feed 1 and 2 mass flows in. The two equations are the sum of mass fractions = 1 and the sum of mass flows calculated = sum of unknowns. Use solver to get the flows for mixer 1 (note: mixer 1 flow out = 8110 lbm/hr).

Hints for 3-17b) second bullet: Setup the mass fractions and mass flows for mixer 2 and enter the relationships for alloy 2 mass fractions and flow rates based on the two streams in (sum of the two/out = fractions), use the 8110 lb/hr from above to solve for feed 5 mass flow given 1E4 target. Use the sum of mass fractions for feed 5 =1 and sum of mass fractions for alloy II =1 as your two equations. Only feed 5 F and K fraction have no mathematical relation and are unknowns. Solve with solver. (note: alloy 2 G mass flow = 2433 lb/hr)

3.17 A bioinstrumentation manufacturer mixes four alloy feeds to continuously produce desired alloys to cast into scalpels and other surgical equipment. (Adapted from Reklatis GV Introduction to Material and Energy Balances, 1983.) (a) Inlet Alloy Feeds 1, 2, 3, and 4 are combined in one mixing unit (Figure 3.30a). The Target Alloy l outlet mass flow rate is 1.00 × 104 Ibm/hr·F, G, H, and K are hypothetical compounds. The weight fractions of compo- nents F, G, H, and K in the Alloy Feeds and Target Alloy I are given in Table 3.10. Calculate the mass flow rates at which the four Alloy Feeds should be supplied to mix to produce the Target Alloy I stream Alloy Feed 1 Alloy Feed 2 Alloy Feed 3 . Alloy Feed 4L MixerTarget Alloy Figure 3.30 Alloy feeds i TABLE 3.10 Alloy Feeds and Target Compositions Component weight fractions Alloy Feed 1 Alloy Feed 2 Alloy Feed 3 Alloy Feed 4 Target AlloyI 4 0.20 0.60 0.20K 0.25 0.250.25 0.60 0.20 0.20 0 0.20 0.60 0 0.20 0 0 0.25 0.20 0.60 0.20 0.20 0.20 0.60 (b) For a different application, Alloy Feed 1 and Alloy Feed 2 are combined in a mixing tank labeled Mixer 1 (Figure 3.30b). The weight fractions of components F, G, H, and K in Alloy Feeds 1 and 2 are given in Table 3.10 The mass fraction of F in the outlet stream from Mixer 1 is 0.50. The outlet stream from Mixer 1 is then combined with Alloy Feed 5 in a second mixing tank labeled Mixer 2 to produce Target Alloy II. Alloy Feed 5 contains only

Explanation / Answer

Let a, b, c and d be flow rates of feeds respectively. After 1 hr, Alloy 1 mass = 10,000

Write the composite mass equations for each feed as follows

.6a + .2b +.2c = 2500

.2a + .6b + .2d = 2500

.2a + .6c + .2d = 2500

.2b + .2c + .6d = 2500

Solve for a, b, c and d. Since the alloy will have same proportion of mixtures, we get a = b = c = d = 2500 lb/hr

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