# UPTU Previous Question Papers

# Hydraulics and Hydraulic machines

# 2006-07

Total Marks : 100

Note : (1) Attempt all questions.

(2) Assume suitable data, if required.

1. Attempt any four parts of the following :

(a) Define – Hydraulic mean radius, hydraulic depth, section factor and most efficient channel cross section.

(b) On what factors does the Manning’s rugosity coefficient depends.

(c) Show that for a rectangular channel with given area is most efficient when hydraulic radius is half of the depth of the flow.

(d) Draw velocity distribution diagram in :

(i) horizontal and vertical sections in a rectangular channel

(ii) effect of curvature in channel.

(e) Obtain formulae for energy correction co-efficient in case of open channel flows.

(1) What do you understand by channel of constant velocity. Derive the relevant formulae.

Attempt any two parts of the following:

(a) An open channel 3 m wide rectangular in shape carries the discharge at normal depth of 1.2 m.

What should be the slope of channel if the Manning’s ‘n’ is 0.014 ?

(b) Prove that the specific energy at critical condition is 1.5 times the critical depth.

(c) Draw the specific energy diagram and describe its various characteristics.

(d) Distinguish between sequent depth and alternate depth in an open channel flow.

(e) A wide rectangular channel carries a flow of 2.75 m^{3}/s per metre width, the depth of flow being 1.5m. Calculate the rise of the floor level required to produce a critical flow condition.

What is the corresponding fall in surface level.

(1) Write an expression for specific force in a rectangular channel and obtain the condition for maximum discharge for a given specific force.

Attempt any four parts of the following :

(a) List the assumptions made in the derivation of dynamic equation of gradually varied flow.

(b) Prove that the slope of free surface in gradually varied flow in open channel flow is given by :

dy ^{s}o~^{s}f dx Q^{2}T gA^{s}

(c) Sketch the G.V.F. profiles produced on

(i) steep slope

(ii) critical slope.

(d) A wide rectangular channel 8 m wide is to be laid at a slope of 1/64 and carries a discharge of 40 m^{3}/s. A barrier across the channel raises the water surface of 3 m just upstream of the barrier. Find the length of surface profile upto the hydraulic jump upstream. Assume Manning’s rugosity coeff. As 0.025.

(e) Describe examples where (i) the upstream end becomes the control section in GVF.

(1) Show that the slope of free surface profile can be expressed by

y_{r}

^{s}o

1-1^/

Where symbols carry the conventional meaning.

Attempt any two parts of the following:

(a) Hydraulic jump is sometimes used as energy dissipator at the toe of the spillway of a dam, why? Discuss different ways for obtaining the hydraulic jump. Prove that relative height of the jump, depend only on flow corresponding supercritical conditions’ Froude Number.

(b) Describe axial and mixed flow pumps. Sketch different characteristic curves for centrifugal pump. How these curves can be used in selecting a pump ?

(c) A tidal estuary is flowing at the rate of 1.8 m/s and depth of flow is 2m. Owing to the tide in the sea the level of water rose rapidly and

the resulting surge took one hour to reach 19.8 km upstream. Compute the height of the bore above the initial depth of bore. Also determine the speed and direction of the flow after the bore has passed.

Attempt any two parts of the following

(a) Draw neat sketches of various shapes of draft tubes. Also, explain the theory of draft tube.

(b) (i) Define and explain – hydraulic efficiency,

mechanical efficiency and overall efficiency in case of turbines. What is the relationship between these three ?

(ii) A Pelton wheel develops 4500 kW under a net head of 125 m while running at a speed of 200 rpm. Assuming K_{y} = 0.98, speed ratio K_{u} = 0.46 and overall

efficiency r|_{0} = 88%, the ratio of nozzle dia to pitch circle dia (d/D)=l/9 determine (a) discharge required (b) dia of wheel

(c) the diameter and no. of jets required.

(c) An inward flow reaction turbine discharges radially and the velocity of flow is constant and equal to the velocity of discharge from the turbine. Show that hydraulic efficiency is given by