The water flowing through a 1.7 cm (inside diameter) pipe flows out through three 1.3 cm pipes. (a) If the flow rates in the three smaller pipes are 26, 19, and 12 L/min, what is the flow rate in the 1.7 cm pipe? (b) What is the ratio of the speed of water in the 1.7 cm pipe to that in the pipe carrying 26 L/min?
Solution:
a) Let the volumetric flows be denoted as Vfm for the master pipe(1.7cm) and Vf1 , Vf2 , Vf3 are volumetric flows of three 1.3cm pipes whose values are 26,19,12L/min respectively.
Since no water is wasted or stored, the sum of volumetric flows in all the three 1.3cm pipes is equal to the volmetric flow of the master pipe.
Therefore, Vfm = Vf1+Vf2+Vf3
Vfm=26+19+12= 57L/min
b) The speed of the water is given by ,
RATIO = velocity of master pipe/velocity of secondary pipe = { 57/ [*(1.72) /4 ] } / { 26/ [*(1.32) /4 ] }
RATIO = { 57/26 }*{ 1.69/2.89 }
Therefore, RATIO = 1.282
**since it is a ratio there are no units.
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