Water of density `p` flows with a linear speed `v` through a horizontal rubber tube having the form of a ring of radius `R`. If the diameter of the tube is `d(ltlt R)`, find the tension in the rubber tube.

Explanation

Mass of water contained in length subtending angle `d theta` at center
`dl=-R d theta`
`dm=rho pi r^(2)dl=rhaopi((d)/(2))^(2) Rd theta=(pi rho d^(2) R)/(4)d theta`
radial component of tension provides centripetal force.
`2T sin((d theta)/(2))=(dmv^(2))/(R )`
`2T(d theta)/(2)=(pi rhod^(2)R)/(4)(v^(2))/(R )d theta`
`T=(pirhod^(2)v^(2)/(4)`
(as `d theta` is small, `sin(d theta)/(2)=(d theta)/(2))`