A: The 68°F refers to water temperature, not air—density is a function of water temperature, and at 68°F water's density is approximately 62.3 lb/ft³. The slight difference between 62.3 and the commonly used 62.4 is negligible for most problems and won't affect the answer choice. The formula Q·ΔH/3960 is appropriate here because you're dealing with water.

A: P1 is at the bottom of the 100-foot-deep lake, so it's the atmosphere pushing down plus 100 feet of water column sitting on that point—the 200-foot elevation difference is handled by the Z term in Bernoulli, not the static pressure term. For friction loss, I'd only reach for the Hazen-Williams equation if the problem specifically gives the C value or asks you to use it; otherwise the Darcy equation or steel pipe friction tables are preferable. The deviation you saw between methods (8.4 vs. 8.1 feet) is trivially small relative to the 200-foot total head, so it doesn't affect the answer.

A: That approach finds only the static pressure difference, not the total head the pump must add—it's missing the elevation change and friction losses, which are often the dominant terms. Any time there's a pump, you need the full Bernoulli equation with the head-added term: HA = (P2−P1)/γ + (V2²−V1²)/2g + (Z2−Z1) + HF. The static pressure difference alone is just one piece of the story.

A: My general guidance is an 8-inch cutoff: for pipes 8 inches or larger, rounding to nominal diameter is fine; for smaller pipes, the difference between nominal and actual can be significant because it gets squared in the area calculation and directly affects velocity. The concern isn't rushing—it's maintaining accuracy on the problems where precision actually matters. Don't let exam anxiety push you to skip details that could change the answer choice.

A: The reference line is arbitrary—once chosen, the pressure at each state is just the column of fluid sitting on that point. P1 is at the bottom of a 100-foot lake, so it has 100 feet of water plus atmosphere pushing down on it; P2 is at the top of an elevated tank, with essentially just one atmosphere (100 feet of air pressure is negligible—about 0.003 ATM). In the delta P subtraction, the atmosphere cancels, and you're left with the net 100-foot water column difference that the pump must overcome.

A: H_A is the head added by a pump, which is very different from head loss H_F—don't confuse them. Without a pump, Bernoulli balances both sides with friction losses on the downstream side; adding a pump introduces an energy input term on the inlet side, which rearranges to: HA = (P2−P1)/γ + (V2²−V1²)/2g + (Z2−Z1) + HF. If there's no pump, HA disappears and you're back to the standard Bernoulli equation with losses.

A: They lead to the same or approximately the same result, so it's your choice—most engineers prefer the steel pipe friction tables for speed when dealing with water in steel pipe. That said, know the Darcy equation thoroughly because if the problem involves a non-steel pipe, you'll be forced to use it. When comparing methods, think about absolute error rather than relative error: a 50% relative difference in a small loss term may be completely insignificant relative to the total system head.

A: These are two separate things: the static pressure at a point is how much fluid column is sitting on it (100 feet of lake water plus atmosphere), while the elevation term Z captures the physical height difference between where you're pumping from and to (200 feet total). They're not the same—don't conflate static pressure with elevation pressure. In the delta P subtraction, atmosphere cancels, leaving just −100 feet as the static pressure contribution, while the elevation term adds +200 feet: the net work the pump must do is 100 feet, which makes intuitive sense.

A: Think of it like a seesaw: the 100-foot column of water sitting on the pump inlet is pushing down and helping the pump, while the pump has to overcome 200 feet of elevation on the other side. The net effect is that the pump only has to supply the additional 100 feet of head—the lake depth helps cancel part of the elevation requirement. Interestingly, it doesn't matter where you locate the pump in the system; the required delta P works out the same regardless.