Fluid Machinery 2018 Question Paper — Government College of Engineeri…

Instructions

• Attempt Five Questions selecting at least two from each section.
• Assume missing data suitably.

Questions

SECTION - A

• Q1. a.. A rectangular plate $1\text{ m}$ wide and $1.5\text{ m}$ deep is held vertically in water so that its upper horizontal edge is $1.25\text{ m}$ below the free water surface. Find the total water pressure on one face of plate, and the depth of center of pressure. Specific wt. of water is $9.81\text{ KN/m}^3$. [10 marks]
• Q1. b.. State Bernoulli's theorem for steady flow of an incompressible fluid. Derive an expression for Bernoulli's theorem from first principle and state the assumptions made for such a derivation. [10 marks]
• Q2. a.. Two reservoirs with a difference in water surface elevation of $10\text{ m}$ are connected by a pipe line ABC which consists of two pipes AB & BC joined in series. Pipe AB is $10\text{cm}$ in dia, $20\text{m}$ long and has a value of $f=0.02$. Pipe BC is of $16\text{cm}$ dia, $25\text{m}$ long and has an $f=0.08$. The junctions with the reservoir and between the pipes are abrupt. i. Calculate the discharge ii. What difference in reservoir elevations is necessary to have a discharge of $15\text{L/S}$? (Include all minor losses) [10 marks]
• Q2. b.. Derive the expression for power transmission through pipes What is the condition for maximum transmission of power and corresponding efficiency of transmission? [10 marks]
• Q3. a.. A trapezoidal channel has side slopes of 3:4 and slope of its bed is 1 in 2000. Determine the optimum dimensions of the channel, if it is to carry water at $0.5\text{ m}^3\text{/s}$. Take Chezy's constant = 80. [15 marks]
• Q3. b.. Explain the terms rapidly varied flow and gradually varied flow. [5 marks]
• Q4. a.. A trapezoidal channel is required to carry $6\text{m}^3\text{/sec}$ of water at a velocity of $1.5\text{m/s}$. Find the most economical cross-section if the channel has side slopes 1 vertical to 2 horizontal. For the same discharge what saving in power would result if this trapezoidal section is replace by rectangular section $1.5\text{m}$ deep and $3\text{m}$ wide? Use C = 55. In Chezy formula. [12 marks]
• Q4. b.. A pitot tube is inserted in a pipe of $300\text{mm}$ dia. The static pressure in a pipe is $100\text{mm}$ of mercury (vacuum). The stagnation pressure at the center of the pipe, recorded by the pitot tube is $0.981\text{ N/cm}^2$. Calculate the rate of flow of water through pipe, if the mean velocity of flow is $0.85$ times the central velocity. Take $C_v = 0.98$. [8 marks]

SECTION - B

• Q5. a.. Show that the force exerted by a jet of water on moving inclined plate in the direction of jet is given by $F_x = \rho a(V - u)^2 \sin^2 \theta$. Where $a = \text{ area of jet}$, $\theta = \text{inclination of plate with the jet and } V = \text{velocity of jet}$. [10 marks]
• Q5. b.. What is a draft tube? Why is it used in a reaction turbine? Describe different types of draft tubes with sketch. [10 marks]
• Q6. a.. Write short note on: i. Froude's law ii. Advantage of Buckingham's pi theorem. iii. Dynamic similarity. [12 marks]
• Q6. b.. In a model test of slip way the discharge and velocity of flow over the model were $2\text{ m}^3\text{/s}$ and $1.5\text{ m/s}$ respectively. Calculate the velocity and discharge over the prototype which is 36 times the model size. [8 marks]
• Q7. a.. A Francis turbine with an overall efficiency of $75\%$ is required to produce $148.25\text{ KW}$ power. It is working under a head of $7.62\text{m}$. The peripheral velocity = $0.26\sqrt{2gH}$ and the radial velocity of flow at inlet is $0.96\sqrt{2gH}$. The wheel runs at $150\text{ rpm}$ and the hydraulic losses in the turbine are $22\%$ of the available energy Assuming radial discharge, determine: i. The guide blade angle ii. The wheel vane angle at inlet iii. Diameter of the wheel at inlet. [10 marks]
• Q7. b.. Define the terms: specific speed and unit speed of turbine. Also derive the expression for specific speed. [10 marks]
• Q8. a.. Draw layout of a hydro electric power plant and explain salient features. [10 marks]
• Q8. b.. A centrifugal pump impeller has an outer dia of $30\text{cm}$ and an inner dia of $15\text{cm}$. The pump runs at $1200\text{rpm}$. The impeller vanes are set at a blade angle of $30^0$ at the outlet. If the velocity of flow id constant at $2.0\text{ m/s}$, calculate: i. The velocity and direction of water at outlet. ii. The head developed, by assuming a manometric efficiency of $0.85$. iii. The blade angle at the inlet. [10 marks]

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