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Department of Mechanical Engineering National University of Singapore
ME 2135 – Fluid Mechanics II– Quiz – Dilip !hah Time Allocated: 40 Minutes
Instructions to Candidates: 1. 2. ". 4.
Answ Answer er ALL ALL quest questio ions ns.. This quiz quiz is equival equivalent ent to 10 10 o! the the course course total total score. score. #nter onl$ onl$ $our metric metric num%er num%er on the to& to& ri'ht corner corner o! this this &a'e. &a'e. (ou are allowe allowed d to re!er re!er to $our $our class lectur lecturee notes. notes.
Q.1 Consider two geometrically similar centrifugal pumps. ne of the pumps !pump 2" is four times larger than the other !pump 1"# i.e. D2 = 4 D1. $oth pumps operate at their BEP point. (i) %f &oth pumps pump water and use the same power # estimate the ratio of flow'rates through the two pumps# i.e. Q1 (Q2. (ii) Compare the rotation rates of the two pumps under these conditions# i.e. N2 / N1. (4 marks) )he non dimensional varia&les are CQ*Q(ND+ , C-*g-(ND and C/*/(0N+D.
2iven3 D * 4D1
5t $E/# C-# CQ and C/ will &e the same for the two pumps. 5lso given is /1 * / . )herefore# C/1 * C/ implies P 1 " ) ρ N 1 D1
=
P 2 "
)
ρ N 2 D2
"
)
N D1 ⇒ 2 = D N 1 2 Therefore
Also C Q1
Q2 Q1
N 2 N 1
)
1 " = = 0.0++ 4
= C Q 2
N 2 D2
"
−4
D1 = = N 1 D1 D2
"
= *.")
′− ∂ − −
Q. )he stream function for an irrotational flow field is given &y
(
ψ = Λ r π α sin π θ where 6 and 7 are constants. Derive the potential α
function for this flow field. Determine the stream function and potential function for 7 * 8(. 9or what value of 7# the given stream function may represent a uniform flow: (6 marks)
u r 1r r r 1 r r Therefore
r cosand v cos f 1 r sin cos f - r , r cos 1
For
α
=
π
2
/
Ψ = Λr 2 sin- 2θ , = 2Λr sin θ cos θ = 2Λ xy Φ = Λr 2 cos- 2θ , = Λr 2 (cos 2 θ − sin 2 θ ) = Λ( x 2 − y 2 ) π