In designing piping systems, it is sometimes desirable to estimate the appropriate pipe length for a given diameter, pump power and flow rate. In such cases, if minor pipe losses are neglected, then the pump head hp matches the frictional head loss hf. i.e.

Consider a pump that delivers 450W to water at 20^oC, which flows in a 15-cm diameter asphalted cast iron horizontal pipe with a speed of u=1.8m/s. What should the length of the pipe be in order to match these conditions?

Note: Use both the Moody diagram and the following empirical relationship to determine the friction factor and comment on the final solutions obtained from the two different approaches.