Question

could you please answer all parts of this question. like and comment are rewarded.

Compulsory question: Al. (a) A fluid satisfies the balance laws at S, pod 1=- Lorem pnds + + L pg av á J., pdv = 0 [10] (i) Explain the physical meaning of each of the terms in the above equations. Explain what has been neglected from the first term on the right-hand side of the first equation. (ii) State the local (differential) version of the second equation. (b) (i) Explain the physical meaning of the condition V.v = 0, where v is the velocity of a fluid. (ii) Consider a fluid flowing through a syringe. Use the condition. v = 0 and the divergence theorem to show that Sunds where S, is a cross-section of the barrel of the syringe, S, is a cross-section of the needle of the syringe, ni is the normal to Si, and n2 is the normal to S3, as shown in the diagram below. Explain your reasoning. ni S2 n2 S [13] (iii) Water is steadily squirted at a speed of 40 cms- from a syringe whose needle is 3 mm in diameter, and whose barrel is 1 cm in diameter. Estimate the speed of the plunger. (c) An aeroplane cruises at a constant speed of 250 ms. The Reynolds number of the air flow is approximately 107, the viscosity of the air is 1.8 10-5Pas, and the circulation of the air flow around the aeroplane's wings is 1.6 x 10^m's! Estimate the mass of the aeroplane. [7]

Answer 1

Page No. @ 0 아 dt -ſpôds + fg dv V av 1 I I I It represents the rate at which momentum of control volume. is changing on It represents the rate force of gravity acting control volume 1 It represents the force acting control votume due to pressure momentum is leaving control volume. on 1.e d at follo v total mass of control volume mass of control volume is constant. le әр at + Befort) b) ن Bino represents the flux of velocity field through a unit. volume. gar no =0 means that an incompressible

flow flux. of velocity Zero. field through unit volume () ... Bon 30 Integrating it over a control volume DvdV V By Gauss's divergence 'ence theorem vñ ds OVES where S = SUS2 g . ñ dst as so fo SI S2 > Replace": ñ M (inward unit surmal) Non IS v . r ds = SH > A vom ds vonds ST S2

(iii) 19 40 см st ni 3 mm Tom 12 v2 = VIA V2 Az 2 Aj V2 V 2 40 cm! (0+3) (1)2 v = 3-6 uns 2