Answer:
The fluid velocity V = 1.98 ft/s
Explanation:
From the information given:
The fluid velocity can be determined from the head-loss [tex]h_L[/tex] of a laminar pipe and it is expressed as:
[tex]h_L = f\dfrac{l\times V^2}{D \times 2g}[/tex]
where;
f = frictional factor ; l = length; D = diameter; V= fluid velocity and g = acceleration due to gravity.
And;
[tex]f = \dfrac{64}{Re}[/tex]
For fluid movement in a laminar flow, the Reynolds number (Re) is usually lesser than 2100.
Given that:
Re = 1508 < 2100 ( laminar flow)
Then;
[tex]f = \dfrac{64}{1508}[/tex]
f = 0.04244
Also;
the head-loss [tex]h_L[/tex] = 6.2 ft
frictional force f = 0.04244
length = 20-ft
acceleration due to gravity (g) = 32.2 ft/s²
Replacing all the values into the equation [tex]h_L = f\dfrac{l\times V^2}{D \times 2g}[/tex]; the fluid velocity is:
[tex]6.2 = 0.04244 \times \dfrac{20 \times V^2}{0.1 \times \dfrac{1}{12} \times 2\times 32.2}[/tex]
[tex]6.2 = 0.04244 \times \dfrac{20 \times V^2}{0.53667}[/tex]
6.2 × 0.53667 = 0.04244 × 20 × V²
3.327354 = 0.8488 × V²
[tex]V^2= \dfrac{3.327354} { 0.8488}[/tex]
[tex]V^2=3.92[/tex]
[tex]V = \sqrt{3.92}[/tex]
V = 1.98 ft/s
