380 POWER PLANT ENGINEERING

and V =
60

πDN

∝ (^) H for prototype.
∴ From the above two equations, we can write
DN
dn

H
h
or
N
n =
d
D
H
h
(b) Quantity q = πdb vf ∝ d^2 h as b ∝ d and vf ∝ h
and Q = πDBVf ∝ D^2 H
∴
Q
q

D^2
d



H
h

D^2
d



.
DN
dn

D^3
d



.
N
n
(c) Power p = 75 m
ρqh

. ηm ∝ ρm. d^2 h. h. hm

and p =
75

ρpQH

. ηp ∝ ρp. D^2 H. H. ηp

∴

p

p

=

p

m

ρ

ρ

.

D^2

d







.

H 3/2

h







.

p

m

η

η

=

pp

mm

ρη

ρη

.

D^2

d







.

H 3/2

h







=

pp

mm

ρη

ρη

.

D^2

d







.

DN^3

dn







= pp

mm

ρη

ρη

.

D^5

d



^

N^3

n





If ρp = ρm

∴

P

p

=

p

m

η

η.

D^5

d







N^3

n







If ηp = ηm which is not the general case

∴

P

p

=

D^2

d







.

H 3/2

h







=

D^5

d







N^3

n







(d) The specific speed for model and prototype should also be same

∴ Ns = ns