A manufacturer of small water pumps lists the performance data for a family of its pumps as a parabolic curve fit, H_available = H₀ – aV̇², where H₀ is the pump’s shutoff head and a is a coefficient. Both H₀ and a are listed in a table for the pump family, along with the pump’s free delivery. The pump head is given in units of feet of water column, and capacity is given in units of gallons per minute.

(a) What are the units of coefficient a? 

(b) Generate an expression for the pump’s free delivery V̇_max in terms of H₀ and a. 

(c) Suppose one of the manufacturer’s pumps is used to pump water from one large reservoir to another at a higher elevation. The free surfaces of both reservoirs are exposed to atmospheric pressure. The system curve simplifies to H_required = (z₂ – z₁) + bV̇². Calculate the operating point of the pump (V̇_operating and H_operating) in terms of H0, a, b, and elevation difference z₂ – z₁.