A rough pipe of 0.5 {m} diameter, 300 {m} length and roughness height of 0.25 {mm}, carries water (kinematic viscosity =0.9 \times 10^{-6} {m}^{2} {s} ) with velocity of 3 {m} {/} {s}. Friction factor ( f) for laminar flow is given \frac{1}\sqrt{f}=2 \log _{10}(\frac{r}{k})+1.74 by f=64 {/} {Re}, and for turbulent flow it is given by \sqrt{f} where, Re= Reynolds number, r= radius of pipe, k= roughness height and g=9.81 {m} {/ } {s}^{2}. The head loss (in {m}, up to three decimal places) in the pipe due to friction is____________.

GATE Civil Engineering (CE) 2018 Shift 2 Solved Paper

Question : 51 of 65

Marks: +1, -0

A rough pipe of

0.5 {m}

diameter,

300 {m}

length and roughness height of

0.25 {mm}

, carries water (kinematic viscosity

=0.9 × 10^{-6} {m}^{2} {s}

) with velocity of

3 {m} {/} {s}

. Friction factor

(

f) for laminar flow is given

\;{1}/{√{f}}=2 \log _{10}(\;{r}/{k})+1.74

f=64 {/} {Re}

, and for turbulent flow it is given by

√{f}

where,

Re=

Reynolds number,

r=

radius of pipe,

k=

roughness height and

g=9.81 {m} {/ } {s}^{2}

. The head loss (in

{m}

, up to three decimal places) in the pipe due to friction is____________.

Solution:

R_{e} \;\; =\;{ρ ⋅ V ⋅ D}/{µ}=\;{V ⋅ D}/{v}=\;{3 ×(0.5)}/{0.9 × 10^{-6}}

\;\; =1.67 × 10^{6}

Means turbulent flow.

\;{1}/{√{f}} \;\; =2 \log _{10} \;{D}/{2 k_{s}}+1.74

\;{1}/{√{f}} \;\; =2 \log _{10} \;{0.5}/{2 × 0.25 × 10^{-3}}+1.74

f \;\; =0.01669

h_{f} \;\; =\;{f ⋅ L ⋅ V^{2}}/{2 g D}=\;{(0.01669)(300)(3)^{2}}/{2 × 9.81 × 0.5}

So,

\;\; =4.594 {m}

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