A water tank filled with solar-heated water at 40°C is to be used for showers in a field using gravity-driven flow. The system includes 35 m of 1.5-cm-diameter galvanized iron piping with four miter bends (90°) without vanes and a wide-open globe valve.

If water is to flow at a rate of 1.2 L/s through the shower head, determine how high the water level in the tank must be from the exit level of the shower.

Disregard the losses at the entrance and at the shower head, and neglect the effect of the kinetic energy correction factor. The density and dynamic viscosity of water at 40°C are rho = 992.1 kg/m3 and μ = 0.653 × 10–3 kg/m·s.

The roughness of galvanized iron pipe is ε = 0.00015 m. Ignore the minor losses. The free surface of the tank must be m above the shower exit to ensure water flow at the specified rate.