Two horizontal pipes of radii 1 cm and 2cm are connected with one-another. Water is flowing through them. If the velocity of water in first pipe is `8 ms^(-1)` and the pressure is `1.0 xx 10^(5) Nm^(-2)`, then pressure (in N `m^(-2)`) and velocity (in `ms^(-1)`) of water in second pipe are (Density of water `= 10^(3) kg m^(-3)`)

Options

A. `1.0 xx 10^(5), 8`
B. `2 xx 10^(5),16`
C. `1.3 xx 10^(5), 2`
D. `1.8 xx 10^(5), 4`

Answer

C

Explanation

According to equation of continuity
`A_(1) v_(1) = A_(2) v_(2) :. (v_(2))/(v_(1)) = (A_(1))/(A_(2)) = (pi r_(1)^(2))/(pi r_(2)^(2)) = ((r_(1))/(r_(2)))^(2) or v_(2) = v_(1) ((r_(1))/(r_(2)))^(2)= 8 ((1)/(2))^(2) = (8)/(4) = 2 ms^(-1)`
From Bernoulli.s theorem, `P_(2) = P_(1) + (1)/(2) rho (v_(1)^(2) - v_(2)^(2))`
`= 1.0 xx 10^(5) + (10)/(2) xx 10^(3) xx (8^(2) -2^(2)) = 1.3 xx 10^(5) Nm^(-2)`