Fluid Mechanics II 2010 (2006 Ad).pdf - DSpace at CUSAT

IV. (a) State and discuss the assumptions made in the derivation of the dynamic equation for
gradually varied flow starting from first principles derive equation for the slope of the
coater surface in gradually varied flow with respect to (i) channel bed (ii) horizontal.
(b) Show that the gradually varied flow equation for flow in a rectangular channel of variable
width B may be expressed as
Qty dB
dY S - +(j
dx
dx
1
n2 B
gie
(a)
OR
Show that the head loss in a hydraulic jump formed in a rectangular channel
VII.
(b)
(vi —V2)3
may be expressed as AE =
2 g(V, - V2).
2
A horizontal rectangular channel 3 m wide and 2 m water depth conveys water at
18 m3/s. If the flow rate is reduced to 2/3 of it's original value, compute the magnitude
and speed of the upstream surge. Assume that the front of the surge is rectangular and
friction in the channel is neglected.
(a) Explain with sketches the working of an oil pressure governor. (7)
(b) Show from the first principles that the peripheral coefficient of a pelton wheel is 0.5. (8)
OR
Show that in a turbine with radial vanes at inlet and outlet and operating under head 'h',
if the velocity of flow at outlet is C times that at inlet, the peripheral velocity `u' and the
hydraulic efficiency 'Rh' are given by
2gh 2
u
-
2 + c 2 tan 2 a ' 2 + c 2 tan2 a
where a is guide de blade angle
Assuming that the radial component of flow of fluid through a centrifugal pump
remains constant and that the fluid enters radially, prove that the ratio of the pressure
head Hp to the velocity head Hv created by an impeller neglecting the losses is given
by Hp ((II—VAcot Pi , where U1 is the speed of impeller at outlet, Vf,
Hv U, +Vf, cot 13
is the veloety of flow and /3 is the exit angle of impeller blades. Hence show that
, — Vf, cot p)
ideal efficiency of the impeller is given by ri =(U.
2U,
OR
Working from the first principles show that, in a single acting reciprocating pump
the work done against pipe friction, if large air vessels are fitted near to the cylinder
on both suction and delivery pipes, compared with that done if there are no air vessels
is (%2 g2).
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