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Water flows in a horizontal tube of vari...

Water flows in a horizontal tube of variable cross-section (figure). The area of cross-section at `x` and `y` are `40 mm^(2)` and `20mm^(2)` respectively. If `10 c c` of water enters per second through `x`, find `(i)` the speed of water at `x`, `(ii)` the speed of water at `y` and `(iii)` the pressure difference `P_(x) - P_(y)`.

Text Solution

Verified by Experts

The correct Answer is:
`(i) 25 cm//s, (ii) 50 cm//s, (iii) 93.75 N//m^(2)`
`A_(1)v_(1) = A_(2)v_(2)`
(i) `10 cm^(3)//s = 40 mm^(2) xx v_(x)` or `v_(x) = 25 cm//s`
`(ii) 10 cm^(3)//s = 20 mm^(2) xx v_(y)` or `v_(y) = 50 cm//s`
`P_(x) + (1)/(2)rhov_(x)^(2) = P_(y) + (1)/(2) rhov_(y)^(2)`
`P_(x) - P_(y) = (1)/(2) rhov _(y)^(2) - (1)/(2) rhov_(x)^(2) = (1)/(2) xx 1000 [((1)/(2))^(2) - ((1)/(4))^(2)]`
or `P_(x) - P_(y) = 93.75 N/m^(2)`.
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