The side wall of a wide vertical vessel of height `h=75 cm` a narrow slit (vertical) running all the way down to the bottom of the vessel.
The length of the slit is `l=50 cm` and the width is `b=1 mm`. With the slit closed, water is filled to the top. Find the resultant reaction force of water coming out as the slit is opened. brgt 
The side wall of a wide vertical vessel of height `h=75 cm` a narrow slit (vertical) running all the way down to the bottom of the vessel.
The length of the slit is `l=50 cm` and the width is `b=1 mm`. With the slit closed, water is filled to the top. Find the resultant reaction force of water coming out as the slit is opened. brgt
The length of the slit is `l=50 cm` and the width is `b=1 mm`. With the slit closed, water is filled to the top. Find the resultant reaction force of water coming out as the slit is opened. brgt
Text Solution
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Let us consider an infinitensimal portion of length `dx` of the slit at a depth `x` below water level. Reaction force due to this portion is given by
`dF=Av^(2)rho=(bdx)2gxrho`
Total reaction force is
`F=intdf=int_(h-t)^(h)2grhob(xdx)`
`=(2grhob)/2[h^(2)-(l-h)^(2)]=grhobl(2h-l)`
`dF=Av^(2)rho=(bdx)2gxrho`
Total reaction force is
`F=intdf=int_(h-t)^(h)2grhob(xdx)`
`=(2grhob)/2[h^(2)-(l-h)^(2)]=grhobl(2h-l)`
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