Fig shows how the stream of water emerging from a faucet "necks down" as it falls . This change in the horizontal cross- sectional area is characteristic of any laminar (nonturbulant) falling stream because the gravitational force increases the speed of the stream . Here the indicated cross-sectional areas are `A_(0) = 1.2 cm^(2)` and `A = 0.35 cm^(2)` . The two levels are separated by a vertical distance h = 45 mm . What is the volume flow rate from the tap ?

Explanation

From Eq. , we have
`A_(0) v_(0) = A v,`
where `v_(0)` and `v` are the water speeds at the levels corresponding to `A_(0)` and A . We can also write , because the water is freely with acceleration g ,
`v^(2) = v_(0)^(2) + 2 gh `
Eliminating v between Eqs. solving for `v_(0)` we obtain .
`v_(0) = sqrt((2 gh A^(2))/(A_(0)^(2) - A^(2)))`
`= sqrt((2) (9.8 m//s^(2)) (0.045 m ) (0.35 cm^(2))^(2))/((1.2 cm^(2))^(2) - (0.35 cm^(2))^(2)))`
`=0.286 m//s = 28.6` cm/s .
From Eq, the volume flow rate , `R_(y)` is then `R_(y) = A_(0) v_(0) (1.2 cm^(2)) (28.6 cm//s)`
`= 34 cm^(3)//s`.