Question

Oil with a kinematic viscosity of 4 10 6 m2 /s fl ows through a smooth pipe 12 cm in diameter at 2.3 m/s. What velocity should water?

Answer 1

Velocity of 5 cm diameter pipe is 1.38 m/s

Step-by-step explanation:

Use following equation of Relation between the Reynolds numbers of both pipes

`Re_(5)` =
`Re_(12)`

`\sqrt{(V_(5)XD_(5) )/(v_(5))}`=
`\sqrt{(V_(12)XD_(12) )/(v_(12))}`

`Re_(5)` = Reynold number of water pipe

`Re_(12)` = Reynold number of oil pipe

`V_(5)` = Velocity of water 5 diameter pipe = ?

`V_(12)` = Velocity of oil 12 diameter pipe = 2.30

`v_(5)` = Kinetic Viscosity of water = 1 x
`10^(-6)`
`m^(2)`/s

`v_(12)` = Kinetic Viscosity of oil = 4 x
`10^(-6)`
`m^(2)`/s

`D_(5)` = Diameter of pipe used for water = 0.05 m

`D_(12)` = Diameter of pipe used for oil = 0.12 m

Use the formula

`\sqrt{(V_(5)XD_(5) )/(v_(5))}`=
`\sqrt{(V_(12)XD_(12) )/(v_(12))}`

By Removing square rots on both sides

`{(V_(5)XD_(5) )/(v_(5))}`=
`{(V_(12)XD_(12) )/(v_(12))}`

`{V_(5)`=
`{(V_(12)XD_(12) )/(v_(12)XD_(5)\\)}`x
`v_(5)`

`{V_(5)`= [ (0.23 x 0.12m ) / (4 x
`10^(-6)`
`m^(2)`/s) x 0.05 ] 1 x
`10^(-6)`
`m^(2)`/s

`{V_(5)` = 1.38 m/s