Answer:
When y = 0.25 ft, velocity gradient = -6 ft/s
When y = 0.5 f, velocity gradient = -1.5 ft/s
Explanation:
Given;
equation for the velocity profile, 3/2 = 4yv
Rearrange this equation, you will get;
[tex]4yv = \frac{3}{2}\\\\v = \frac{3}{2} *\frac{1}{4y} \\\\v = \frac{3}{2}(\frac{1}{4} )(\frac{1}{y} )\\\\v = \frac{3}{8}y^{-1}\\\\ gradient \ of \ velocity \ = \frac{dv}{dy} \\\\\frac{dv}{dy} = -1(\frac{3}{8})y^{-2}[/tex]
When y = 0.25 ft
[tex]\frac{dv}{dy} = -1(\frac{3}{8})(0.25)^{-2}\\\\\frac{dv}{dy} = -6 \ ft/s[/tex]
When y = 0.5 ft
[tex]\frac{dv}{dy} = -1(\frac{3}{8})(0.5)^{-2}\\\\\frac{dv}{dy} = -1.5 \ ft/s[/tex]
