The pressure rise, Ap, across a pump can be expressed as Ap = f(D, p, w, Q), where D is the impeller diameter, p the fluid density, w the rotational speed, and Q the flowrate. Determine a suitable set of dimensionless parameters.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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Please fast answer these 2 questions please i need both. Only final answer needed.
The pressure rise, Ap, across a pump can be
expressed as
Δρ -f D, ρ, ω, Q) ,
where D is the impeller diameter, p the fluid
density, w the rotational speed, and Q the flowrate.
Determine a suitable set of dimensionless
parameters.
Ap
D² po?
D3 @
O Ap
D²@?
D3
Ο Δp
PQ
D²o
Ο Δρ
po
O Ap
PQ
D²o³
Transcribed Image Text:The pressure rise, Ap, across a pump can be expressed as Δρ -f D, ρ, ω, Q) , where D is the impeller diameter, p the fluid density, w the rotational speed, and Q the flowrate. Determine a suitable set of dimensionless parameters. Ap D² po? D3 @ O Ap D²@? D3 Ο Δp PQ D²o Ο Δρ po O Ap PQ D²o³
Assume that the flowrate, Q, of a gas from a
smokestack is a function of the density of the
ambient air, Pa, the density of the gas, pg, within
the stack, the acceleration of gravity, g, and the
height and diameter of the stack, h and d,
respectively. Use Pa, d, and g as repeating variables
to develop a set of pi terms that could be used to
describe this problem.
Pg
h
Qd³12
1/2
8,
Pa´d
(hpg
P
dpa
d512 g1/2
Pg h
P
Pa´d
d$/2 g1/2
Pg
h
Vdg
Pa´d
hpg
evdg = p
dpa.
Transcribed Image Text:Assume that the flowrate, Q, of a gas from a smokestack is a function of the density of the ambient air, Pa, the density of the gas, pg, within the stack, the acceleration of gravity, g, and the height and diameter of the stack, h and d, respectively. Use Pa, d, and g as repeating variables to develop a set of pi terms that could be used to describe this problem. Pg h Qd³12 1/2 8, Pa´d (hpg P dpa d512 g1/2 Pg h P Pa´d d$/2 g1/2 Pg h Vdg Pa´d hpg evdg = p dpa.
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