A sand-bed filter with diameter of 1.6 m is used for waste water filtration. Initially the fixed

bed contains a 0.5 m-thick layer of fine sand (dv = 0.25 mm) on top of a 0.5 m-layer of coarse

sand (dv = 1 mm). The initial bed voidage in each layer is 0.4, and the sand particles have

specific gravity of 1.6 and sphericity of 0.8, which is independent of particle size. After a

period of operation, the sand bed needs to be cleaned by backwashing with upward flow of

clean water which causes the bed to fluidise.

a. Calculate the minimum flow rate of clean water (in m3 /h) required for fluidising the bed for

backwashing.

b. Determine the maximum backwashing flow rate (in m3 /h) allowable for safely fluidising the

bed.

c. In practice, it is desirable that the fine sand layer is expanded to three (3) times its settled

depth during backwashing. Determine the flow rate of clean water required, the overall

depth of the bed and the pressure drop across the bed during backwashing. Particulate

fluidisation may be assumed and this assumption will need to be verified.