Question

A pipe carrying water from a tank 18.0 m tall must cross 3.05 102 km of wilderness to reach a remote town. Find the radius of the pipe so that the volume flow rate is at least 0.0500 m3/s. (Use the viscosity of water at 20°C, 1.0 ✕ 10−3 N · s/m2.)

Answer 1

2.165 cm

Step-by-step explanation:

`\rho` = Density of water = 1000 kg/m³

g = Acceleration due to gravity = 9.81 m/s²

h = Height of tank = 18 m

P = Pressure =
`\rho gh`

Q = Flow rate = 0.05 m³/s

`\eta` = Viscosity of water =
`1* 10^(-3)\ Ns/m^2`

r = Radius of pipe

From Poiseuille's Law we have

`Q=(\pi Pr^4)/(8\eta l)\\\Rightarrow r=\left((8Q\eta l)/(\pi P)\right)^{(1)/(4)}\\\Rightarrow r=\left((8* 0.05* 1* 10^(-3)* 305)/(\pi 1000* 9.81* 18)\right)^{(1)/(4)}\\\Rightarrow r=0.02165\ m`

The radius of the pipe should be 2.165 cm