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
[tex]Q_T = Q_1+Q_2+Q_3[/tex]
[tex]Q_T = 27+19+12[/tex]
[tex]Q_T = 58L/min[/tex]
PART B) The radius would be given between another pipe with a flow rate of 27L / min.
For proportionality ratio we have to
[tex]\frac{Q_T}{Q'} = \frac{A_TV_T}{A'V'}[/tex]
[tex]\frac{V_T}{V'} = \frac{A_'Q_T}{A_TQ'}[/tex]
[tex]\frac{V_T}{V'} = \frac{(\pi r_T^2)Q_T}{(\pi r'^2)Q'}[/tex]
[tex]\frac{V_T}{V'} = \frac{1.2*^2 58}{1.8^2 27}[/tex]
[tex]\frac{V_T}{V'} = 0.9547[/tex]
