B.TECH - Semester 4 fluid mechanics 2 Question Paper 2020 (sep)
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- 404 : FLUID MECHANICS - II (C) (2008 Scheme) Time : 3 Hours Max. Marks : 80 Instructions :
- All questions under Part A are compulsory.
- Answer any one full question from each module under Part B.
- (a) Differentiate uniform and non-uniform flow. What is meant by normal depth in a channel?
- (b) Define most efficient channel section. Derive the expression for most efficient rectangular Section.
- (c) Define specific energy in open channel and discuss specific energy curve.
- (d) List the different assumptions made in deriving dynamic equation for gradually varied flow.
- (e) Explain different types of $M$ profiles in prismatic channels with practical examples.
- (g) Explain classification of turbines.
- (h) Define specific speed of pumps and derive an expression for the same. $$ \text { ( } 8 \times 5=40 \text { Marks) } $$
- (b) A rectangular channel 12 m wide carries a discharge of $200 \mathrm{~m}^{3} / \mathrm{s}$. Find the critical depth and critical velocity. What slope will produce this velocity in the channel if Manning's $\mathrm{n}=0.02$ ?
- (b) A rectangular channel 7.5 m wide carries $12 \mathrm{~m}^{3}$ of water per second with a velocity of $1.5 \mathrm{~m} / \mathrm{sec}$. Compute the specific energy. Also find the depth of flow in the channel when the specific energy would be minimum. What will be the value of critical velocity as...
- (d) Differentiate between laminar boundary layer and laminar sub layer.
- (i) boundary layer thickness at the end of the plate, (ii) shear stress at the middle of the plate, and (iii) total drag per unit length on the sides of the plate. Take the kinematic viscosity of air as 0.15 stokes. OR
- (b) A 2 m wide channel having side slope $1 \mathrm{H}: 2 \mathrm{~V}$ carries water at a depth of 1 m . Calculate the discharge if the bed slope is 1 in 625 and $\mathrm{n}=0.03$. Also calculate the average shear stress at the channel boundary.
- (a) A triangular channel with side slope $1 \mathrm{H}: 1 \mathrm{~V}$ and longitudinal slope of 0,001 discharges water at a rate of $0.2 \mathrm{~m}^{3} / \mathrm{sec}$. Determine whether the channel is mild, steep or critical. Assume Manning's $\mathrm{n}=0.015$. For what range of depths will the ...
- (c) Derive the dynamic equation of gradually varied flow.
- 404 : FLUID MECHANICS - II (C) (2013 Scheme) Time : 3 Hours Max. Marks : 100 PART - A Answer all questions. Each question carries 4 marks.
- (a) Derive the expression for specific speed of a certrifugal pump.
- (b) A 2 m wide rectangular channel has a flow with a velocity of $2 \mathrm{~m} / \mathrm{s}$ and depth of 1.3 m . The rate of inflow at the upstream end is suddenly increased to an extent that the depth is doubled in magnitude. Estimate the absolute velocity of the resulting surge and the new disch...
- (a) For a Pelton wheel, a jet of cross section area $0.15 \mathrm{~m}^{2}$ is discharging through the nozzle at the rate of $0.18 \mathrm{~m}^{3} / \mathrm{s}$ under a head of 32 m . The shaft power is 44 kW and mechanical efficiency is $94 \%$. Calculate the power lost (i) in the nozzle and (ii) in...
- (b) A pelton wheel is to be designed for the following data. Power to be developed $=500 \mathrm{~kW}$, Net available need $=290 \mathrm{~m}$, Speed $=500$ r.p.m, Ratio of jet diameter to wheel diameter $=1 / 8$, overall efficiency $82 \%$. Find the number of jet, diameter of the jet diameter of th...
- (b) Explain the different types of hydraulic jump.
- (a) A trapezoidal channel is to be designed to convey $50 \mathrm{~m}^{3} / \mathrm{s}$ of water at a velocity of $2 \mathrm{~m} / \mathrm{s}$. The bed width to depth ratio is to be 8 and the side slopes are to be $1 \mathrm{H}: 1 \mathrm{~V}$. It will be lined with a material whose Manning's $n=0.0...
- (a) Explain Buckingham's $\pi$-Theorem.
- (b) Air flows over a plate 1 m long at a velocity of $6 \mathrm{~m} / \mathrm{sec}$. Determine the
- (a) Derive the conditions for a hydraulically efficient rectangular channel section.
- (f) Discuss the dimensionless numbers.
- (a) A flow of $0.11 \mathrm{~m}^{3} / \mathrm{sec}$ flows in a rectangular flume of width 0.60 m . Determine the bottom slope necessary to have uniform flow at a depth of 0.30 m . Also compute the conveyance of flow. Take Chezy's constant as 55 .
- (a) An irrigation channel of trapezoidal section with side slopes of 3 horizontal to 2 vertical carries discharge of $12 \mathrm{~m}^{3} / \mathrm{s}$. Bed slope of channel is 1 in 6000 . The channel is to be lined with a material having roughness coefficient $\mathrm{n}=0.015$. Design the most econ...
- (a) Derive an expression for pressure difference $\Delta \mathrm{p}$ in a pipe of diameter d and length 1 due to viscous flow depends on the velocity $V$, viscosity $\mu$ and density $\rho$ using Buckingham's $\pi$ theorem.
- (b) An air duct of cross-sectional area $1 \mathrm{~m}^{2}$ at inlet is reduced to $0.5 \mathrm{~m}^{2}$ at a $45^{\circ}$ bend. Find the magnitude and direction of the resultant force exerted by air on the bend if the velocity of flow at inlet is $12 \mathrm{~m} / \mathrm{s}$ and the pressure is 25...
- (a) Define (i) Dimensional homogeneity (ii) Undistorted models (iii) Reynold's model law and (iv) Scale effect in models.
- (b) A river 50 m wide and a bed slope of 1 in 10,000 have uniform flow at 4 m depth. Compute the length of backwater curve produced by an afflux of 3 m on downstream side. Identify the surface profile also. Take $\mathrm{n}=0.03$.12
- (b) A horizontal jet of water 2 cm dia. and velocity $10 \mathrm{~m} / \mathrm{s}$ strikes normally at the centre of a 20 cm size square plate having weight of 98 N , suspended vertically by a hinge on top edge. Find the horizontal force applied at the lower edge to keep the plate vertical. If the p...
- (a) Explain the effect of friction and acceleration in suction and delivery pipes of a reciprocating pump.
- (b) Calculate the diameter and speed of the runner of a Kaplan turbine developing 6000 kW under an effective head of 5 m . Overall efficiency of the turbine is $90 \%$. The dia. of boss is 0.4 times the external dia. of runner. The speed ratio is 2.0 and flow ratio is 0.6 . What is the specific spee...
- (a) Derive a relation between Chezy's and Manning's constants
- (e) Explain the effect of cavitation in centrifugal pumps. $$ P A R T-B \quad(5 \times 4=20 \text { Marks }) $$ Answer any one full questions from each Module. Each question carries 20 marks.
- (b) The cross-section of an open channel consists of semi-circular bottom 1.2 m in diameter and with vertical sides. If the rate of flow is $0.402 \mathrm{~m}^{3} / \mathrm{s}$ and the bed slope is 1 in 2500, calculate the centre line depth of water. Assume manning's $\mathrm{n}=0.011$. 10
- (a) Derive an equation for the absolute velocity and celerity of a positive surge wave.
- (b) At a certain section $M$ in rectangular channel of bed width $2 m$ the depth of flow is 1.2 m . When the flow rate is $6 \mathrm{~m}^{3} / \mathrm{s}$, estimate the distance from M to another section N where the depth is 1.4 m . The bed slope is 0.002 and Manning's $\mathrm{n}=0.015$. Take two s...
- (a) In order to estimate the energy loss in a pipeline of 1 m diameter, through which kerosine of specific gravity 0.8 and dynamic viscosity 0.02 poise is to be transported at the rate of $2 \mathrm{~m}^{3}$ per second, model tests were conducted on a 0.1 m diameter pipe using water at $20^{\circ} \...
- (b) A model boat, $1: 100$ size of its prototype has 0.12 N of resistance when simulating a speed of $5 \mathrm{~m} / \mathrm{s}$ of the prototype. Water is the fluid in both cases. What is the corresponding resistance in the prototype? Neglect the frictional forces.
- (a) A jet of water having a velocity of $40 \mathrm{~m} / \mathrm{s}$ strikes a curved vane, which is moving with a velocity of $20 \mathrm{~m} / \mathrm{s}$. The jet makes an angle of 30 degree with the direction of motion of vane at inlet and leaves at an angle of 90 degree to the direction of mot...
- (b) What is a draft tube? Explain the different types of draft tubes with sketch.
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