Filter beds must periodically be backwashed to remove the material that

accumulates. In this system, backwash water $($which can be assumed to have the

standard properties of water$)$ is supplied through the base of the tank at an inlet

gauge pressure head of $40\mathrm{.}0m($of water$).$ The backwash water flows upwards

through the filter bed, and exits via flowing over a weir as shown in the figure below

a free surface is present at the top of the water body.

The filter bed is $4\mathrm{.}0m$ deep, and has a cross sectional area of $6\mathrm{.}5m^2.$ The particles

in the filter bed are spherical, have an average diameter of $2\mathrm{.}8mm,$ and the void

fraction in the bed is $0\mathrm{.}38.$

Determine the volume flow rate of backwash water through the filter $($in $\frac{m^3}{s}).$ For

the purpose of calculation, you may assume that the system is at steady state, the

filter bed is clean, and you may neglect the effect of any accumulated matter.