Turbulent flow in horizontal pipes, a fluid is flowing with a mass flow rate w in a smooth horizontal pipe of length L and diameter D as the result of a pressure difference P0 - PL. The flow is known to be turbulent. The pipe is to be replaced by one of diameter D/2 but with the same length. The same fluid is to be pumped at the same mass flow rate w. What pressure difference will be needed? 

(a) Use Eq. 6.2-12 as a suitable equation for the friction factor. 

(b) How can this problem be solved using Fig. 6.2-2 if Eq. 6.2-12 is not appropriate?