Question

Water flows through a horizontal 60 mm diameter galvanized iron pipe at a rate of 0.02 m3/s. If the pressure drop is 135 kPa per 10 m of pipe, do you think this pipe is
a) a new pipe,
b) an old pipe with somewhat increased roughness due to aging or
c) a very old pipe that is partially clogged by deposits. Justify your answer.

Answer 1

Answer:

pipe is old one with increased roughness

Explanation:

discharge is given as

$V =\frac{Q}{A} = \frac{ 0.02}{\pi \4 \times (60\times 10^{-3})^2}$

V = 7.07  m/s

from bernou;ii's theorem we have

$\frac{p_1}{\gamma} +\frac{V_1^2}{2g} + z_1 = \frac{p_2}{\gamma} +\frac{V_2^2}{2g} + z_2 + h_l$

as we know pipe is horizontal and with constant velocity so we have

$\frac{P_1}{\gamma } + \frac{P_2 {\gamma } + \frac{flv^2}{2gD}$

$P_1 -P_2 = \frac{flv^2}{2gD} \times \gamma$

$135 \times 10^3 = \frac{f \times 10\times 7.07^2}{2\times 9.81 \times 60 \times 10^{-5}} \times 1000 \times 9.81$

solving for friction factor f

f = 0.0324

fro galvanized iron pipe we have $\epsilon = 0.15 mm$

$\frac{\epsilon}{d} = \frac{0.15}{60} = 0.0025$

reynold number is

$Re =\frac{Vd}{\nu} = \frac{7.07 \times 60\times 10^{-3}}{1.12\times 10^{-6}}$

Re = 378750

from moody chart

$For Re = 378750 and \frac{\epsilon}{d} = 0.0025$

$f_{new} = 0.025$

therefore new friction factor is less than old friction factoer hence pipe is not new one

now for Re = 378750 and f = 0.0324

from moody chart

we have $\frac{\epsilon}{d} =0.006$

$\epsilon = 0.006 \times 60$

$\epsilon = 0.36 mm$

thus pipe is old one with increased roughness