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Water (density rho) is flowing through t...


Water (density `rho`) is flowing through the uniform tube of cross-sectional area A with a constant speed v as shown in the figure. Find the magnitude of force exerted by the water on the curved corner of the tube is (neglect viscous forces)

Text Solution

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`|overline(DeltaP)_(x)|=mvsin60^(@)=(sqrt(3))/(2)mv`
`|overline(DeltaP)_(y)|=(mv)/(2)=(3)/(2)mvimplies|overline(DeltaP)_("net")=sqrt(DeltaP_(x)^(2)+DeltaP_(y)^(2))=sqrt((9)/(4)+(3)/(4))mv`
`|overline(DeltaP)_(y)|=sqrt(3)mvimplies|overline(DeltaF)_("net")|=sqrt(3)((dm)/(dt))v=sqrt(3)rhoAv^(2)`
(Since, `dm=A(vdt)rhoimplies(dm)/(dt)=Arhov`)
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