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Sma2110:Applied Mathematics Ii Question Paper
Sma2110:Applied Mathematics Ii
Course:Bachelor Of Computer Science
Institution: Meru University Of Science And Technology question papers
Exam Year:2013
QUESTION ONE (30 MARKS)
a) In a pipe of 300mm diameter the maximum velocity of flow is found to be 2m/s. if the flow in the pipe is laminar, find; i. The average velocity and the radius at which it occurs. (4 Marks) ii. The velocity at 50mm from the wall of the pipe. (3 Marks) b) Determine the direction and amount of flow per metre width between two parallel plates when one is moving relative to the other with velocity of 3m/s in the negative direction, if ?? ?? = -100 × 106??/3 and ?? = 0.4 poise and distance between the plates 1mm. (5 Marks) c) Water at a rate of 0.0006 litre/sec is flowing through a sandy specimen of 8cm height and 45??2 cross-sectional area under a constant head of 7cm. Determine the coefficient of permeability. (4 Marks) d) In a two-dimensional incompressible flow the fluid velocity components are given by = ?? - 4 ???? = - - 4??. i. Show that the flow satisfies the continuity equation. (3 Marks) ii. Obtain the expression for the stream function. (3 Marks) iii. Obtain the expression for the velocity potential. (3 Marks) e) If a 40mm diameter cylinder is immersed in a stream having a velocity of 1.0m/s, determine the radial and normal components of velocity at a point on a streamline where r=50mm and ?? = 135°, measured from the positive x –axis. (5 Marks)
QUESTION TWO (20 MARKS)
a) Briefly explain the meaning of the following terms i. Source (1 Mark)
2
ii. Sink (1 Mark) iii. Doublet (1 Mark) b) A source of strength 10m2s-1 at (1,0) and a sink of the same strength at (-1,0) are combined with a uniform of 25m/s in the x-direction. Determine the size of Rankine body formed by the flow and the difference in pressure between a point for upstream in the uniform flow and the point(1,1) . (12 Marks) c) A steel sphere of 4mm diameter falls in glycerine at a terminal velocity of 0.04m/s. assuming stokes law is applicable, determine i. Dynamic viscocity of glycerine. (3 Marks) ii. Drag force. (2 Marks)
QUESTION THREE (20 MARKS)
a) A liquid of viscosity of 0.9 poise is filled between two horizontal plates 10mm apart. If the upper plate is moving at 1m/s with respect to the lower plate which is stationary and the pressure difference between two sections 60m apart is 60kN/m2, determine i. The velocity distribution ii. The discharge per unit width. iii. The shear stress on the upper plate. (10 Marks) b) An oil of viscocity a poise and specific gravity 0.9 is flowing through a horizontal pipe of 60mm diameter. If the pressure drop in 100m length of the pipe is 1800KN/m2, determine i. The rate of flow of oil. (4 Marks) ii. The total frictional drag over 100m length. (3 Marks) iii. The velocity gradient at the pipe wall. (3 Marks)
QUESTION FOUR (20 MARKS)
Derive the Navier-stokes equations for a three dimensional fluid motion.
QUESTION FIVE (20 MARKS)
Consider flow between two parallel plates for which the lower plate is along the line y = 0. The distance between the plates is b. The upper plate is along the line y = b. If the upper plate is moving at a constant velocity U and the lower plate is stationary and the plates are considered infinite in extend, find
i. The expression for velocity distribution. (12 Marks) ii. The expression for shear stress distribution (8 Marks)
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