Question

Water at 4.4°C is to flow through a horizontal, commercial steel pipe having a length of 305 m at the rate of 150 gal/min. If a head of water of 6.1 m is available to overcome the friction loss F, calculate the pipe diameter.

Answer 1

Answer:

d = 70.5 mm

Explanation:

given,

length of pipe = 305 m

discharge rate = 150 gal/min

pipe diameter = ?

1 gal/min = 6.30902 ×  10⁻⁵ m³/s

150 gal/min = 150 × 6.30902 ×  10⁻⁵ m³/s

                   = 9.46 × 10⁻³ m³/s

$h = \dfrac{flv^2}{2gd}$

$h = \dfrac{flv^2}{2gd}$

Q = A V

$h = \dfrac{fl(\dfrac{Q}{A})^2}{2gd}$

$h = \dfrac{fl(\dfrac{Q}{\dfrac{\pi}{4}d^2})^2}{2gd}$

$h= \dfrac{8flQ^2}{\pi^2gd^5}$

f = 0.048 from moody chart using P/D = 0.00015

$\dfrac{1}{d^5}= \dfrac{6.1\times \pi^2\times 9.8}{8\times 0.048\times 305\times 0.00946^2}$

d = 70.5 mm

Diameter of the pipe is equal to 70.5 mm