Answer:203.60 N
Explanation:
Given
[tex]V_{inlet}[/tex]=3 m/s
[tex]d_{inlet}[/tex]=6 cm
[tex]d_{outlet}[/tex]=2 cm
Using continuity equation
[tex]A_{inlet}V_{inlet}=A_{outlet}V_{outlet}[/tex]
[tex]\frac{\pi \times d_{inlet}^2}{4}\times 3[/tex]=[tex]\frac{\pi \times d_{outlet}^2}{4}\times V_{outlet}[/tex]
[tex]V_{outlet}[/tex]=27 m/s
Horizontal Force required to hold elbow=Change in momentum of water
initial momentum=[tex]\rho \times A_{inlet}\times V_{inlet}=10^{3}\times \frac{\pi}{4}6^2\times 3^{2}\times 10^{-4}[/tex]
Final Momentum=[tex]\rho \times A_{outlet}\times V_{outlet}=10^{3}\times \frac{\pi}{4}2^2\times 27^{2}\times 10^{-4}[/tex]
Force required=[tex]10^{3}\times \frac{\pi }{4}\times 10^{-4}\left [ 27^{2}\times 2{2}-6{2}\times 3{2}\right ][/tex]=203.60 N
