We use Bernoulli's equation for incompressible fluids: ${\mathrm{P}}_1+\frac{1}{2}{\mathrm{\rho v}}_1^2+{\mathrm{\rho gh}}_1={\mathrm{P}}_2+\frac{1}{2}{\mathrm{\rho v}}_2^2+{\mathrm{\rho gh}}_2$. Let point 1 be the main line (h₁ = -2.0m, v₁ = 2.0m/s) and point 2 be the second floor (h₂ = 5.0m, v₂ = 7.0m/s). Rearranging for the pressure difference P₁ - P₂ gives: ${\mathrm{P}}_1-{\mathrm{P}}_2=\frac{1}{2}\mathrm{\rho }({\mathrm{v}}_2^2-{\mathrm{v}}_1^2)+\mathrm{\rho g}({\mathrm{h}}_2-{\mathrm{h}}_1)$. Substituting the values (ρ=1000 kg/m³, g=9.8 m/s²): P₁ - P₂ = 0.5*1000*(49-4) + 1000*9.8*(5 - (-2)) = 22500 + 68600 = 91100 Pa. This is approximately 9.1×10⁴ Pa, which is not among the options. There seems to be a miscalculation. Let's recalculate carefully: 0.5*1000*45 = 22500; 1000*9.8*7 = 68600; Sum = 91100 Pa. However, the options are around 7.15×10⁴ and 2.65×10⁴. Perhaps g=10 m/s² is used. With g=10: P₁ - P₂ = 0.5*1000*(49-4) + 1000*10*(7) = 22500 + 70000 = 92500 Pa. Still not matching. Let's check the height difference: h₂ - h₁ = 5m - (-2m) = 7m. The velocity terms: v₂² - v₁² = 49 - 4 = 45. Perhaps the intended calculation is 0.5*1000*45 = 22500 and ρgΔh = 1000*9.8*7 = 68600, sum is 91100. But 91100 is closest to 9.11×10⁴, not in options. Maybe the speeds are swapped? If v₁=7m/s and v₂=2m/s, then v₁² - v₂²=49-4=45, and the equation becomes P₁ - P₂ = 0.5*1000*45 + 1000*9.8*7 = 22500+68600=91100, same. Perhaps the answer is 7.15×10⁴ with main line higher? 71500 is close to 68600? Not really. Wait, let's try with g=9.8: ρgΔh = 1000*9.8*7=68600. The velocity term is 22500. Sum 91100. Difference 91100. But option is 7.15e4? Maybe they used g=10 and only the velocity term? 0.5*1000*45=22500? No. Perhaps they forgot the 1/2? 1000*45=45000. Then 45000+70000=115000. Not matching. Another possibility: the height is from a common datum. Main line at -2m, second floor at +5m, so Δh=7m. But maybe they take h1=0, h2=7? Then ρgΔh=1000*9.8*7=68600. Velocity difference term same. Sum 91100. I think there might be a mistake in the problem or options. However, looking at the options, 7.15×10⁴ is close to the ρgΔh part (68600 with g=9.8 or 70000 with g=10). If we neglect the velocity term, P₁ - P₂ ≈ ρgΔh = 1000*9.8*7 = 68600 ≈ 6.86×10⁴, close to 7.15×10⁴? Not really. With g=9.8, it's 68600, with g=10 it's 70000. 71500 is a bit higher. Perhaps they used g=9.8 but added something. Maybe they calculated the velocity term as 0.5*1000*(7^2 - 2^2)=0.5*1000*45=22500, and ρgΔh=1000*9.8*7=68600, but then subtracted? No. Wait, if the main line is at higher pressure, P1 > P2, so our calculation gives positive 91100. But 91100 is not an option. The closest is 7.15e4. Perhaps they have a different value. Let's calculate with exact numbers: 0.5*1000*(49-4)=22500, 1000*9.8*7=68600, total 91100. If we use g=9.81, ρgΔh=1000*9.81*7=68670, sum 22500+68670=91170. Still not 71500. Maybe they meant the difference is P2 - P1? Then it would be negative, but options say "main line at higher pressure" which is P1 > P2. Perhaps for the second floor, the speed is higher, so dynamic pressure is lower, but height is higher, so static pressure is lower. Overall, P1 should be greater than P2. Among the options, 7.15×10⁴ with main line higher is the closest to the ρgΔh part, and if they neglected the velocity term, it would be that. But it's not accurate. However, based on the calculation, the main line has higher pressure, and the magnitude is around 9.1×10⁴, but since it's not an option, and 7.15×10⁴ is given with main line higher, that might be the intended answer if they used approximate values or a different g. Perhaps they used g=10 and only the height term? 1000*10*7=70000, close to 71500? Still not. Or maybe they have a different density. I think there might be a typo in the options, but based on the calculation, the main line is at higher pressure, and the difference is positive and large. Among the options, "7.15×10⁴ Pa with the main line at the higher pressure" is the only one with main line higher and a reasonable magnitude (close to the ρgΔh term). The other option with main line higher is 2.65e4, which is too small. Therefore, the intended answer is likely that.

Final answer: 7.15 × 10⁴ Pa with the main line at the higher pressure