Consider a heat exchanger that has 1000, \(2.5 \mathrm{~cm}\) diameter smooth tubes in parallel, each \(6 \mathrm{~m}\) long. The total water flow of \(1 \mathrm{~m}^{3} / \mathrm{s}\) at \(10^{\circ} \mathrm{C}\) flows through the tubes. Neglecting entrance and exit losses, determine:

a. The pressure drop (in \(\mathrm{kPa}\) ).

b. The pumping power required (in \(\mathrm{kW}\) ).

c. The pumping power for the same flow rate if solid deposits from the water build up on the inner surface of the pipe with a thickness of \(1 \mathrm{~mm}\) and an equivalent roughness of \(0.4 \mathrm{~mm}\).