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Unformatted text preview: ( 3)
ρv 2 A2 ρv 2 Fy € 2 The above expression can be made comparable to the Fx expression if we get an expression for p2/ρv22.
This can be simply obtained by dividing (2) by ρv22 /p1 :
2 €2
p
p2
p1
1 v1 0.7 4 p1 1
1
1 =
+ − 1 =
+ (0.7 2 ) − 1 = 0.7 4 1 2 + 1 −
4 2
ρv 2 2 ρv 2 2 2 v 2 ρv12 ρv1 2 0.7 ( ) ‐1.6 This gives the final expression for Fy in terms of the inlet variables: Fy € 2
1 ρv A1 = p F
A2 v 2 2
1
1
( ) = 2y
=
1 + 0.7 4 1 2 − 1.6 ( 4 )
2
2
ρv A2 A1 v1
ρv 2 A2 0.7
0.7 ρv1 Fy
2
2 (d) Now that the Fx and Fy components due to the walls have been found the angle with which they act is: €
θ = tan −1 € 0.49 p1 1.265 + ρv 2 π
ρv1 A1 π
1
−
− ≅ tan−1
Fx 2 −(1 + p1 ) 2 ρv12 A1 ρv12 Fy
2 No numerical values were given, thus the exact angle cannot
be determined. However, the range that the angle must be
as follows (measured counterclockwise from +yaxis to be
positive) as Fx is <0):
π
2 € <θ <0...
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This note was uploaded on 01/24/2014 for the course ME 106 taught by Professor Morris during the Spring '08 term at University of California, Berkeley.
 Spring '08
 Morris

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