Answer:
a)54L/min
b)0.845
Explanation:
a) A x V=[tex]A_1V_1+ A_2V_2+A_3V_3[/tex]
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 => [tex]\frac{\pi }{4} d^2[/tex] x v
d= 2 cm
[tex]\frac{\pi }{4} d^2[/tex] x v = 54
v= [tex]\frac{4}{\pi }[/tex] x [tex]\frac{54}{2^2}[/tex]
-> [tex]A_1[/tex] x [tex]V_1[/tex]=27L/min => [tex]\frac{\pi }{4} d_1^2[/tex] x [tex]v_1[/tex]
[tex]d_1[/tex]= 1.3cm
[tex]\frac{\pi }{4} d^2[/tex] x [tex]v_1[/tex] = 27
[tex]v_1[/tex]= [tex]\frac{4}{\pi }[/tex] x [tex]\frac{27}{1.3^2}[/tex]
Next is to find the ratio of speed i.e [tex]\frac{v}{v_1}[/tex]
[tex]\frac{4}{\pi }[/tex] x [tex]\frac{54}{2^2}[/tex] / [tex]\frac{4}{\pi }[/tex] x [tex]\frac{27}{1.3^2}[/tex] => [tex]\frac{54}{27}[/tex] [tex]\frac{1.3^2}{2^2}[/tex]
[tex]\frac{v}{v_1}[/tex]= 0.845
