174
(4.35)
The expression (4.35) can be brought into form (4.33) with very good approximation as
(4.36)
With (4.36), the results become very good for the data of Exercise 4.8.1. Only the
last terms in (4.35) and (4.36) differ (velocity by the formulae of De Saint Venant
and Bernoulli) with values 256.78 m/s (exact) and 256.24 m/s (approximate).
References
Fox RW, Pritchard PJ, McDonald AT (2010) Introduction to fluid mechanics, 7th edn. Wiley, ISBN
978-0-470-23450–1
Imrie BW (1973) Compressible fluid flow. Butterworth & Co, ISBN 0-408-70434–9
So
1
2
4
2
2
1
2
2
1
1
1
v
p
p
1
(
)
[ 1
,
2
1
p
g
g
g
b r r
g
r
−
−
=
−
−
and
1
1
2
2 th
4
2
1
1
2
1
p
p
1
m
A
2
1
.
1
p
1
(
)
g
g
g
r
g
r
b r r
−
=
−
−
−
2 th
4
2
m
2 1
1
2 p
m
A
.
1
(
)
D
r
r
b r r
=
−
4 Compressible Fluids
(4.35)
The expression (4.35) can be brought into form (4.33) with very good approximation as
(4.36)
With (4.36), the results become very good for the data of Exercise 4.8.1. Only the
last terms in (4.35) and (4.36) differ (velocity by the formulae of De Saint Venant
and Bernoulli) with values 256.78 m/s (exact) and 256.24 m/s (approximate).
References
Fox RW, Pritchard PJ, McDonald AT (2010) Introduction to fluid mechanics, 7th edn. Wiley, ISBN
978-0-470-23450–1
Imrie BW (1973) Compressible fluid flow. Butterworth & Co, ISBN 0-408-70434–9
So
1
2
4
2
2
1
2
2
1
1
1
v
p
p
1
(
)
[ 1
,
2
1
p
g
g
g
b r r
g
r
−
−
=
−
−
and
1
1
2
2 th
4
2
1
1
2
1
p
p
1
m
A
2
1
.
1
p
1
(
)
g
g
g
r
g
r
b r r
−
=
−
−
−
2 th
4
2
m
2 1
1
2 p
m
A
.
1
(
)
D
r
r
b r r
=
−
4 Compressible Fluids