Tutorial 1 Mathematical Modeling and Engineering Problem Solving

Tutorial 1 Mathematical Modeling and Engineering Problem Solving Lecture Notes Dr. Rakhmad Arief Siregar Universiti Malaysia Perlis Applied Numerical Method for Engineers 1

P. 1. 1 n n n Water accounts for roughly 60% of total body weight. Assuming it can be categorized into six regions, the percentages go as follows. Plasma claims 4. 5% of the body weight and is 7. 5% of total body water. Dense connective tissue and cartilage occupies 4. 5% of the total body weight and 7. 5% of the total body water. Interstitial lymph is 12% of the body weight, which is 20% of the total body water and 4. 5% total body weight. If intracellular water is 33% of the total body weight and transcellular water is 2. 5% of the body water, What percent of total body weight must the transcellular water be? What percent must the transcellular water be? 2

Solution 1. 1 Components Total Body Weight Total Body Water 1 Plasma 4. 5% 7. 5% 2 Dense 4. 5% 7. 5% 3 Interstitial 12% 20% 4 Inaccessible 4. 5% 7. 5% 5 Intracellular 33% 55? % 6 Trancellular 1. 5? % 2. 5% 60% 100% Total 3

P. 1. 2 n n A group of 30 students attend a class in a room that measures 10 m by 8 m by 3 m. Each student takes up about 0. 075 m 3 and gives out about 80 W of heat (1 W = 1 J/s). Calculate the air temperature rise during the first 15 minutes of the class if the room is completely sealed and insulated. 4

Notes n n Assume the heat capacity, Cv , for air is 0. 718 k. J/(kg K) Assume air is an ideal gas at 20 C and 101. 325 k. Pa. The heat absorbed by the air Q is related to the mass of the air, m, the heat capacity, and the change in temperature by the following relationship: The mass of air can be obtained from the ideal gas law: Mwt: 28. 97 kg/kmol (air) R: 8. 314 k. Pa m 3/(kmol K) 5

Solution 1. 2 n Compute total heat absorbed Q of students n Computer the mass n Compute change of temperature 6

Solution 1. 2 The temperature rise after 15 minutes: n T = (20 C +273. 15) + 10. 50615 T = 303. 65615 K or n T = 30. 50615 C n 7