Answer:
2.165 cm
Explanation:
[tex]\rho[/tex] = Density of water = 1000 kg/m³
g = Acceleration due to gravity = 9.81 m/s²
h = Height of tank = 18 m
P = Pressure = [tex]\rho gh[/tex]
Q = Flow rate = 0.05 m³/s
[tex]\eta[/tex] = Viscosity of water = [tex]1\times 10^{-3}\ Ns/m^2[/tex]
r = Radius of pipe
From Poiseuille's Law we have
[tex]Q=\frac{\pi Pr^4}{8\eta l}\\\Rightarrow r=\left(\frac{8Q\eta l}{\pi P}\right)^{\frac{1}{4}}\\\Rightarrow r=\left(\frac{8\times 0.05\times 1\times 10^{-3}\times 305}{\pi 1000\times 9.81\times 18}\right)^{\frac{1}{4}}\\\Rightarrow r=0.02165\ m[/tex]
The radius of the pipe should be 2.165 cm
