Water is being filtered through a packed bed to remove ions to form deionized water. The bed is 50 cm in diameter, and the packing contains spherical particles with a diameter of 2.5 mm. The porosity of the bed is 0.4. The length of the bed is 3 m. The water is pumped from an atmospheric pressure reservoir through the packed bed and into an elevated atmospheric pressure container. The height difference between the water level in the reservoir and the water level in the container is 4 m. The pipeline is 40 m long (excluding the length of the bed) and has a constant diameter of 100 mm. To measure the volumetric flow rate, we use a 25 mm circular, square-edged orifice with a manometer containing an immiscible fluid with a specific gravity of 13.6 connected across the orifice. The difference in fluid levels in the manometer is 2.5 cm. You need to determine the required power (kW) of a 60% efficient pump for this duty. Notes: a) Neglect any minor friction losses b) Assume that the orifice meter does not cause any permanent pressure loss. The density of water 1000 kg/m3 and the viscosity of water is 0.001 kg/(m*s). The pipe is made of commercial steel.