[ Re = \frac\rho V D\mu = \frac1000 \times 2.546 \times 0.11\times10^-3 = 254,600 \ (>4000 \Rightarrow \textTurbulent) ]
Relative roughness: $\epsilon/D = 0.00026 / 0.1 = 0.0026$. Colebrook equation: $\frac1\sqrtf = -2\log\left(\frac0.00263.7 + \frac2.51254600\sqrtf\right)$. Iterate (or use Moody chart): Initial guess $f_0 = 0.026$. RHS: $-2\log(0.0007027 + 2.51/(254600\sqrt0.026)) = -2\log(0.0007027 + 1.91\times10^-5) = -2\log(0.0007218) = -2(-3.1415) = 6.283 \Rightarrow f = 1/6.283^2 = 0.0253$. Converged: $f \approx 0.0254$. fluid mechanics course
[ V = \fracQA = \frac0.02\pi(0.1^2)/4 = \frac0.020.007854 = 2.546\ \textm/s ] [ Re = \frac\rho V D\mu = \frac1000 \times 2
[ h_f = f \fracLD \fracV^22g = 0.0254 \times \frac2000.1 \times \frac(2.546)^22 \times 9.81 ] [ h_f = 0.0254 \times 2000 \times 0.330 = 16.76\ \textm ] [ \Delta p = \rho g h_f = 1000 \times 9.81 \times 16.76 = 164,400\ \textPa = 164.4\ \textkPa ] RHS: $-2\log(0