Pipes & Cisterns

Direction matters.

• Inlet (Fill): Positive Work (+).
• Outlet (Empty): Negative Work (-).
• Net Rate: Rate(In) - Rate(Out).

If a leak increases filling time.

• Method: Find Leak Efficiency by subtraction.
• $Eff(Leak) = Eff(Net) - Eff(Pipe)$. Usually Net is slower.

To find Total Liters.

• Logic: Capacity = Rate of Pipe (L/min) $\times$ Time taken by THAT Pipe (min).
• First find Time of Pipe X using Ratios, then multiply by its tangible rate.

Positive and Negative cycles.

• Trap: Tank fills only at the END of a positive cycle. Do not divide directly.
• Hack: Subtract last positive work from Total. Divide rest by Cycle. Then add last step manually.

Complex combinations.

• Rule: Sum all efficiencies algebraically.
• If Net Eff is negative, tank will EMPTY (Total Work = Initial Fills).

Pipes open at different times.

• Method: Calculate partial work done before all open.
• Subtract from Total. Solve rest with Combined Efficiency.

Flow rate depends on pipe Cross-Section Area.

• Rule: Rate $\propto d^2$ (square of diameter).
• If diameter doubles ($d \to 2d$), Flow becomes $4x$. Time becomes $1/4$.