Question

The water flowing through a 2.0 cm (inside diameter) pipe flows out through three 1.3 cm pipes. (a) If the flow rates in the three smaller pipes are 27, 16, and 11 L/min, what is the flow rate in the 2.0 cm pipe? (b) What is the ratio of the speed of water in the 2.0 cm pipe to that in the pipe carrying 27 L/min?

Answer 1

a)54L/min

b)0.845

Step-by-step explanation:

a) A x V=
`A_1V_1+ A_2V_2+A_3V_3`

where suffix 1,2,3 refers to the three pipes.

=27L/min+16L/min+11 L/min

=54L/min

b) A x V=54L/min =>
`(\pi )/(4) d^2` x v

d= 2 cm

`(\pi )/(4) d^2` x v = 54

v=
`(4)/(\pi )` x
`(54)/(2^2)`

->
`A_1` x
`V_1`=27L/min =>
`(\pi )/(4) d_1^2` x
`v_1`

`d_1`= 1.3cm

`(\pi )/(4) d^2` x
`v_1` = 27

`v_1`=
`(4)/(\pi )` x
`(27)/(1.3^2)`

Next is to find the ratio of speed i.e
`(v)/(v_1)`

`(4)/(\pi )` x
`(54)/(2^2)` /
`(4)/(\pi )` x
`(27)/(1.3^2)` =>
`(54)/(27)`
`(1.3^2)/(2^2)`

`(v)/(v_1)`= 0.845