In a closed loop of pipe segments, what is the algebraic condition on head losses around the loop?

• A. The sum of head losses around the loop equals zero
• B. The sum of head losses is equal to the pump head added
• C. The sum of velocity heads around the loop equals zero
• D. Head losses are always positive

Answer: (A)

In a closed loop, energy must balance as you travel around and come back to the same point. Head is a measure of energy per unit weight, and head losses represent the energy that gets dissipated as friction and turbulence. As you go around the loop, you lose energy along each segment; finishing the loop returns you to the same location with the same energy, so the total change in head must be zero. That means the algebraic sum of head losses around the loop is zero (any energy added by a pump would appear as a head gain and would balance the losses to keep the sum zero). This captures energy conservation in a closed piping loop.