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Sma2109:Applied Mathematics Question Paper
Sma2109:Applied Mathematics
Course:Bachelor Of Computer Science
Institution: Meru University Of Science And Technology question papers
Exam Year:2010
QUESTION ONE – (30 MARKS)
(a) Distinguish between Fluid Kinematics and fluid dynamics. (2 Marks) (b) Calculate the specific weight, specific mass, specific volume of 6m3 and a weight of 44KN. (4 Marks) (c) State Newton’s law of viscosity. (2 Marks) (d) If the velocity distribution over a plate is given by ?? = 2 3 ?? - ??2 in which u is the velocity in m/s at a distance y metre above the plate, determine the shear stress at ?? = 0 and ?? = 0.15??. Take dynamic viscosity of fluid as 8.63 poises. (6 Marks) (e) Find the velocity and acceleration at a point 1,2,3 after 1 sec for a 3 – dimensional flow given by ?? = ???? + ??, ?? = ???? - ??, ?? = ????. (6 Marks) (f) Find the expression for the power ??, developed by a pump when ?? depends upon the head H, the discharge Q and specific weight ?? of the fluid. (5 Marks) (g) Water is flowing through a pipe of diameter 30cm at a velocity of 4m/s. Find the velocity of oil flowing in another pipe of diameter 10cm, if the condition of dynamic similarity is satisfied between the two pipes. The viscosity of water and oil is given as 0.01 poise and 0.025 poise and specific gravity of oil is 0.8. (5 Marks)
QUESTION TWO – (20 MARKS)
(a) Briefly discuss the difference between the following types of flow (i) Steady and unsteady flows. (2 Marks) (ii) Laminar and Turbulent flows (2 Marks)
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(iii)Rotational and irrotational flows (2 Marks)
(b) Derive the continuity equation in three-dimensions. (10 Marks) (c) In a three-dimensional incompressible flow, the velocity components in ?? ?????? ?? directions are ?? = ????3 - ????2 + ????2, ?? = ????3 - ????2 + ????2??. Determine the missing component of velocity distribution such that continuity equation is satisfied. (4 Marks) QUESTION THREE – (20 MARKS)
(a) A fluid flow field is given by ?? = ??2???? + ??2???? - 2?????? + ????2 ?? (i) Prove that it is a case of possible steady incompressible fluid flow. (4 Marks) (ii) Calculate the velocity and acceleration at the point (2, 1, 3). (6 Marks)
(b) In a two-dimensional incompressible flow, the fluid velocity components are given by ?? = ?? - 4?? ?????? ?? = -?? - 4??
(i) Show that velocity potential exists and determine its form. (3 Marks) (ii) Find the stream function. (3 Marks)
(c) A stream function is given by ?? = 5?? - 6??. Calculate the velocity components, magnitude and direction of the resultant velocity at any point. (4 Marks)
QUESTION FOUR – (20 MARKS)
(a) Briefly explain the meaning of the following terms (i) Dimensional analysis (1 Mark) (ii) Dimensional homogeneity (1 Mark) (b) The resisting force R of a supersonic plane during flight can be considered as dependent upon the length of the aircraft L, velocity V, air viscosity ??, air density ?? and bulk modulus of air K. Express the functional relationship between these variables and the resisting force. (6 Marks) (c) State Buckingham’s II Theorem (2 Marks) (d) The efficiency of ?? a fan depends on density ??, dynamic viscosity ?? of the fluid , angular velocity w, diameter D of the rotor and discharge Q. Express ?? in terms of dimensionless parameters. (10 Marks)
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