Question

The water flowing through a 1.8 cm (inside diameter) pipe flows out through three 1.2 cm pipes. (a) If the flow rates in the three smaller pipes are 27, 19, and 12 L/min, what is the flow rate in the 1.8 cm pipe? (b) What is the ratio of the speed of water in the 1.8 cm pipe to that in the pipe carrying 27 L/min?

Answer 1

To solve this problem it is necessary to apply the Discharge of flow equations.

From the theory the flow rate is defined as

Q = AV

Where,

A =Area

V = Velocity

PART A) The question is telling us about the total fluid flow rate then

$Q_T = Q_1+Q_2+Q_3$

$Q_T = 27+19+12$

$Q_T = 58L/min$

PART B) The radius would be given between another pipe with a flow rate of 27L / min.

For proportionality ratio we have to

$\frac{Q_T}{Q'} = \frac{A_TV_T}{A'V'}$

$\frac{V_T}{V'} = \frac{A_'Q_T}{A_TQ'}$

$\frac{V_T}{V'} = \frac{(\pi r_T^2)Q_T}{(\pi r'^2)Q'}$

$\frac{V_T}{V'} = \frac{1.2*^2 58}{1.8^2 27}$

$\frac{V_T}{V'} = 0.9547$