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(e) The dynamic coefficient of viscosity # (viscosity of a fluid) is found from the formula: Fis the force exerted on the liquid, A is the cross sectional area of the path, v is the fluid velocity andlis the distance travelled by the fluid. Using dimensional analysis techniques, determine the equation that governs pand its dimensions using the results of (b) and the equation in c dearly showing all steps in the dimensional analysis.

(e) The dynamic coefficient of viscosity # (viscosity of a fluid) is found from the formula: Fis the force exerted on the liquid, A is the cross sectional area of the path, v is the fluid velocity andlis the distance travelled by the fluid. Using dimensional analysis techniques, determine the equation that governs pand its dimensions using the results of (b) and the equation in c dearly showing all steps in the dimensional analysis.

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Answer Task (1), part (e).

Task 1 (a) A low voltage transformer manufacturing line has a purchase order of 1700 piece. If the manufacturing line production rate is 22 piece per minute use dimensional analysis techniques to determine the time taken to produce the requested transformers to the nearest minute in hours and minutes. (b) Assume that the production time of a transformer can be given by the following formula: t = Gm2v-312 Where m is the mass of the transformer in kg, vis the velocity of the manufacturing line in m/s and l is the length of the production line in meters. Find the dimensions of G. (9) In b, if m = 220 grams,1= 10.2 m, v=2.3 m/s and time is 30.1 ms. Find G? Page 4 of 14 (d) The force, F, of a turbine generator is a function of density p, area A and velocity v. By assuming F= ap" A*pe and dimensional homogeneity, find a, b and c and express Fin terms of p, A and v. (a, a, b and c are real numbers). Make the following assumptions to determine the dimensionless parameter: F=1kNifthe scalar values of pAv= 1milli. (e) The dynamic coefficient of viscosity u (viscosity of a fluid) is found from the formula: Fis the force exerted on the liquid, A is the cross sectional area of the path, v is the fluid velocity andlis the distance travelled by the fluid. Using dimensional analysis techniques, determine the equation that governs u and its dimensions using the results of (b) and the equation in c, clearly showing all steps in the dimensional analysis.
Transcribed Image Text:Task 1 (a) A low voltage transformer manufacturing line has a purchase order of 1700 piece. If the manufacturing line production rate is 22 piece per minute use dimensional analysis techniques to determine the time taken to produce the requested transformers to the nearest minute in hours and minutes. (b) Assume that the production time of a transformer can be given by the following formula: t = Gm2v-312 Where m is the mass of the transformer in kg, vis the velocity of the manufacturing line in m/s and l is the length of the production line in meters. Find the dimensions of G. (9) In b, if m = 220 grams,1= 10.2 m, v=2.3 m/s and time is 30.1 ms. Find G? Page 4 of 14 (d) The force, F, of a turbine generator is a function of density p, area A and velocity v. By assuming F= ap" A*pe and dimensional homogeneity, find a, b and c and express Fin terms of p, A and v. (a, a, b and c are real numbers). Make the following assumptions to determine the dimensionless parameter: F=1kNifthe scalar values of pAv= 1milli. (e) The dynamic coefficient of viscosity u (viscosity of a fluid) is found from the formula: Fis the force exerted on the liquid, A is the cross sectional area of the path, v is the fluid velocity andlis the distance travelled by the fluid. Using dimensional analysis techniques, determine the equation that governs u and its dimensions using the results of (b) and the equation in c, clearly showing all steps in the dimensional analysis.
(b) Given: t= Gm3 v12 Solution: using dimentional analysis, ITI = IG||M [LT"|*ILF ITI |G| = IG| = |Mi LT] (c) Given: m = 220 gm I= 10.2 m v = 2.3 m/ sec t= 30. I ms Solution: as, t= Gmi v 30. I x 10- = Gx (220 × 10-) x (2.3)-3 x (10. 2) G = 30.1x10 (220bc10 )x(2.3)'x(10.2) G= 16 x 10-3 (kg ms-2)
Transcribed Image Text:(b) Given: t= Gm3 v12 Solution: using dimentional analysis, ITI = IG||M [LT"|*ILF ITI |G| = IG| = |Mi LT] (c) Given: m = 220 gm I= 10.2 m v = 2.3 m/ sec t= 30. I ms Solution: as, t= Gmi v 30. I x 10- = Gx (220 × 10-) x (2.3)-3 x (10. 2) G = 30.1x10 (220bc10 )x(2.3)'x(10.2) G= 16 x 10-3 (kg ms-2)
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