정답: 2번

원관의 지름 \(D = 400 \, \text{mm} = 0.4 \, \text{m}\)
관의 길이 \(L = 100 \, \text{m}\)
수송 시간 \(t = 2 \, \text{시간} = 2 \times 3600 = 7200 \, \text{초}\)
수송 부피 \(V = 300 \, \text{m}^3\)
관마찰계수 \(f = 0.02\)
물의 밀도 \(\rho = 1000 \, \text{kg/m}^3\)
중력 가속도 \(g = 9.81 \, \text{m/s}^2\)

1.  **유량 (\(Q\)) 계산:**
    \(Q = \frac{V}{t} = \frac{300 \, \text{m}^3}{7200 \, \text{s}} = \frac{1}{24} \, \text{m}^3/\text{s} \approx 0.04167 \, \text{m}^3/\text{s}\)

2.  **관 단면적 (\(A\)) 계산:**
    \(A = \pi \left(\frac{D}{2}\right)^2 = \pi \left(\frac{0.4 \, \text{m}}{2}\right)^2 = \pi (0.2 \, \text{m})^2 = 0.04\pi \, \text{m}^2 \approx 0.12566 \, \text{m}^2\)

3.  **유속 (\(v\)) 계산:**
    \(v = \frac{Q}{A} = \frac{1/24 \, \text{m}^3/\text{s}}{0.04\pi \, \text{m}^2} = \frac{1}{0.96\pi} \, \text{m/s} \approx 0.3316 \, \text{m/s}\)

4.  **달시-바이스바흐(Darcy-Weisbach) 식을 이용한 수두손실 (\(h_f\)) 계산:**
    \(h_f = f \frac{L}{D} \frac{v^2}{2g}\)
    \(h_f = 0.02 \times \frac{100 \, \text{m}}{0.4 \, \text{m}} \times \frac{(1/(0.96\pi) \, \text{m/s})^2}{2 \times 9.81 \, \text{m/s}^2}\)
    \(h_f = 0.02 \times 250 \times \frac{1/(0.96\pi)^2}{19.62}\)
    \(h_f = 5 \times \frac{1/(0.9216\pi^2)}{19.62}\)
    \(h_f = 5 \times \frac{1/(0.9216 \times 9.8696)}{19.62}\)
    \(h_f = 5 \times \frac{1/9.098}{19.62} = 5 \times \frac{0.1099}{19.62} \approx 5 \times 0.005601 \approx 0.028005 \, \text{m}\)

5.  **압력손실 (\(\Delta P\)) 계산:**
    \(\Delta P = \rho g h_f\)
    \(\Delta P = 1000 \, \text{kg/m}^3 \times 9.81 \, \text{m/s}^2 \times 0.028005 \, \text{m}\)
    \(\Delta P \approx 274.77 \, \text{Pa}\)

가장 가까운 보기 값은 275 Pa이다.