Correct Answer - Option 1 : 0.993 m of water

**Concept:**

Reynolds number is given by

\(Re = \frac{{\rho VD}}{\mu }=\frac{VD}{ν}\)

where, ρ = Density of fluid, V = velocity of fluid, D = Diameter of pipe, μ = Dynamic viscosity of the fluid and ν = kinematic viscosity of fluid.

**1 Stokes = 10**^{-4} m^{2}/sec.

The darcy-Weisbach formula for head loss due to friction is,

\(h_f = \dfrac{4flV^2}{2gD}\)

where, f = Darcy's coefficient of friction, l = length of the pipe, v = velocity of the fluid in the pipe, D = diameter of the pipe.

**Calculation:**

**Given:**

D = 200 mm, V = 3 m/s, L = 5 m,

kinematic viscosity of water as 0.01 stoke,

g = 9.81 m/s2 and (6 × 105)0.3 = 54.13

\(f=0.02+\frac{0.09}{Re^{o.3}}\)

Reynolds number is given by

\(Re=\frac{VD}{ν}\)

\(Re=\frac{3\times 0.2}{0.01\times10^{-4}}=6\times10^5\)

Given \(f=0.02+\frac{0.09}{Re^{0.3}}\)

\(f=0.02+\frac{0.09}{(6\times10^5)^{0.3}}=0.02+\frac{0.09}{54.13}=0.02166\)

The darcy-Weisbach formula for head loss due to friction is,

\(h_f = \dfrac{4flV^2}{2gD}\)

\(h_f = \dfrac{4\times 0.02166\times 5\times 3^2}{2\times 9.81\times 0.2}=0.993\;m\; of\;water\)