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I Semester M.E. (Civil) Water Resources Engg. Degree Examination, March 2013 2K8 WR 104 : ADVANCED FLUID MECHANICS Time : 3 Hours

Max. Marks : 100

Instructions : 1) Answer any five full questions. 2) Assume any missing data suitably. 3) Use of relevant statistical tables/charts is permitted. 1. a) Derive the three dimensional continuity equation and explain its significance.

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b) Calculate the velocity gradient at distances of 0, 100 and 160 mm from the boundary if the velocity profile is a parabola with the vertex 160 mm from the boundary, where the velocity is 1.20 m/s. Also calculate the shear stresses at these points if the fluid has a viscosity of 1 N-s/m2. 10 2. a) Derive expressions for stream function and velocity potential for : i) Uniform flow and ii) Source.

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b) Obtain the equation of the dividing streamline for the flow resulting from a superposition of a free stream at 20 m/s on a two dimensional source with a strength of 10 m2/s. Sketch the flow pattern. 10 3. a) Show that in case of steady laminar flow through a circular pipe, the average velocity is half the maximum velocity. 12 b) A viscous liquid of specific gravity 0.90 and kinematic viscosity 2.9 × 10 – 4 m2/s flows through a horizontal pipe 100 mm diameter, velocity along the axis is 1.85 m/s, find i) Shear stress along the pipe surface. ii) Discharge. iii) Power required per km length of the pipe. iv) Whether the flow is laminar or not.

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P.T.O.

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4. a) Explain the concepts of i) Energy correction factor and ii) Momentum correction factor.

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⎛y = ⎜ ⎟ where, V is the Vmax ⎝ D ⎠ velocity at distance y from the bed of the channel and Vmax is the velocity at the free liquid surface, distance D above the bed. Determine the velocity distribution coefficients. 10

b) The velocity in an open channel is given by

V

1 ⎞ 4

5. a) Derive an expression for the hydraulic exponent for uniform flow.

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b) A trapezoidal channel having a bottom width of 6 m and side slopes 2H : 1V is laid on a bed slope of 0.0016. If it carries a uniform flow of water at the rate of 10 m3/s, compute the normal depth of flow i) Using section factor tables, and ii) By plotting conveyance vs depth of flow. Take Manning’s n as 0.025. 6. a) Explain the water surface profiles in mild sloping channels with neat sketches. Give examples of each profile.

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b) A rectangular channel 18 m wide and having a bed slope of 1 in 6400 flows with a normal depth of 2 m. At a certain section the depth of flow is 2.8 m. How far upstream or downstream of this section will the depth be 3 m ? Use step method and take two steps. Manning’s roughness coefficient is 0.015. 10 7. a) Explain the graphical integration method of computation of gradually varied flow profile. 10 b) A trapezoidal channel having a bottom width of 6 m, side slope 2H : 1V, Manning’s ‘n’ 0.025 and bed slope of 0.0016 carries a discharge of 10 m3/s. Compute the backwater profile created by a dam which backs up water to a depth of 2 m immediately behind the dam. Use graphical integration method. 10 8. a) Derive an expression for the loss of energy due to a hydraulic jump in a rectangular channel.

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b) A rectangular channel with a width of 2.5 m and bed slope of 1 in 100 carries a discharge of 7 m3/s. A weir constructed in the channel raises the water level to 2 m in the channel. How far upstream of the weir will a jump occur ? Assume Manning’s n = 0.012. 10

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