9.3 Solutions
403
∴
dy
dr
=
ω 2 r
g
y =
dy =
ω 2
g
r dr + c
y =
ω 2 r 2
2g
+ c
y = 0, r = 0, c = 0
y =
1
2
ω 2 r 2
g
Figure of revolution of the curve is a paraboloid.
9.3.2 Torricelli’s Theorem
9.16 Using Bernoulli’s equation
P 2 +
1
2
ρv
2
2 = P 1 +
1
2
ρv
2
1
3.1 × 10
5
+
1
2
× 1000v
2
2 = 3.5 × 10
5
+ 0
v 2 = 8.94 m/s
9.17 (a) Use Bernoulli’s equation at two points A and B at height h A and h B ,
respectively, Fig. 9.7.
P + ρgh A = P + ρgh B +
ρv 2
2
(1)
where P is the atmospheric pressure, ρ is the density of water and v is the
efflux velocity.
Fig. 9.7
403
∴
dy
dr
=
ω 2 r
g
y =
dy =
ω 2
g
r dr + c
y =
ω 2 r 2
2g
+ c
y = 0, r = 0, c = 0
y =
1
2
ω 2 r 2
g
Figure of revolution of the curve is a paraboloid.
9.3.2 Torricelli’s Theorem
9.16 Using Bernoulli’s equation
P 2 +
1
2
ρv
2
2 = P 1 +
1
2
ρv
2
1
3.1 × 10
5
+
1
2
× 1000v
2
2 = 3.5 × 10
5
+ 0
v 2 = 8.94 m/s
9.17 (a) Use Bernoulli’s equation at two points A and B at height h A and h B ,
respectively, Fig. 9.7.
P + ρgh A = P + ρgh B +
ρv 2
2
(1)
where P is the atmospheric pressure, ρ is the density of water and v is the
efflux velocity.
Fig. 9.7