Mercury flows at a speed of 20 cm/s in a pipe with conducting walls of 5 cm diameter. The pipe is in the gap between the pole pieces of an electromagnet, the magnetic field in the gap having induction of 0.6 T. Will the magnetic field affect the hydraulic friction coefficient? The conductivity of mercury is `10^(6)ohm^(-1).m^(-1)`.

Answer

It will [Hint. Find the Stewart number]

Explanation

First find the Reynolds number.
`Re=(rhovl)/(eta)=(13.6xx10^(3)xx5xx10^(-2)xx0.2)/(1.55x10^(-3))=8.8xx10^(4)gtgt2300`.
Hence the flow is turbulent and it should be assessed with the aid of the Stewart number:
`N=(gammaB^(2)l)/(rhov)=(1.05xx10^(6)xx0.36xx5xx10^(-2))/(13.6xx10^(3)xx0.2)=7`
But the Stewart number represents the ratio of the magnetic force to the resistance of pressure. Hence, in this case the magnetic force will appreciably affect the coefficient of hydraulic friction.