Problem 4.79

Prévia do material em texto

Problem 4.79 [Difficulty: 2]
Given: Water flow through nozzle
Find: Force to hold nozzle
Solution:
Basic equation: Momentum flux in x direction for the elbow
Assumptions: 1) Steady flow 2) Incompressible flow 3) Uniform flow
Hence Rx p1g A1⋅+ p2g A2⋅+ V1 ρ− V1⋅ A1⋅( )⋅ V2 cos θ( )⋅ ρ V2⋅ A2⋅( )⋅+= Rx p1g− A1⋅ ρ V22 A2⋅ cos θ( )⋅ V12 A1⋅−⎛⎝ ⎞⎠⋅+=
From continuity V2 A2⋅ V1 A1⋅= s
o
V2 V1
A1
A2
⋅= V1
D1
D2
⎛⎜⎝
⎞
⎠
2
⋅= V2 1.5
m
s
⋅ 30
15
⎛⎜⎝
⎞
⎠
2
⋅= V2 6
m
s
⋅=
Hence Rx 15− 103×
N
m2
⋅ π 0.3 m⋅( )
2⋅
4
× 1000 kg
m3
⋅ 6 m
s
⋅⎛⎜⎝
⎞
⎠
2
π 0.15 m⋅( )2⋅
4
× cos 30 deg⋅( )⋅ 1.5 m
s
⋅⎛⎜⎝
⎞
⎠
2
π .3 m⋅( )2⋅
4
×−
⎡⎢⎣
⎤⎥⎦×
N s2⋅
kg m⋅×+=
Rx 668− N⋅= The joint is in tension: It is needed to hold the elbow on against the high pressure, plus it generates the large
change in x momentum