Answer:
a) since u from equation1 and u from equation2 are not the same ( 1.7825 ft/s ≠ 3.165 ft/s ) then this equation is not valid for any system of units.
b) The velocity according to the equation at y=0 is equal to 0.81 ft/sec but since the fluid is flowing on flat surface which is stationary, this value is wrong hence the equation is NOT CORRECT
Explanation:
Given that;
range ⇒ 0 < y < 0
1ft is given by the equation u = 0.81 + 9.2y + (4.1 × 10³y³)
so u=velocity of water at different layers
y= height of the layer
a)
consider BG system of units
u(ft/s) = 0.81 + 9.2y + (4.1 × 10³y³)
and consider y=0.05 ft
u = 0.81 + 9.2(0.5) + (4.1 × 10³(0.5³)
u = 0.81 + 0.46 + 0.5125
u = 1.7825 ft/s lets say this is equation 1
now consider the SI system units
u(m/s) = 0.81 + 9.2y + (4.1 × 10³y³)
also consider y=0.05ft
1ft = 3.048×10⁻¹ (from conversion table)
so 0.05ft = 0.01524m
we substitute
u(m/s) = 0.81 + 9.2(0.01524m) + (4.1 × 10³(0.01524m)³)
u = 0.81 + 0.1402 + 1.4512×10⁻²
u = 0.9647 m/s
1m/s = 3.281 ft per seconds ( conversion table)
so
0.9647 m/s = 0.9647(3.281)
u = 3.165 ft/s lets say this is equation 2
now since u from equation1 and u from equation2 are not the same ( 1.7825 ft/s ≠ 3.165 ft/s ) then this equation is not valid for any system of units.
b)
we know that the velocity of water at the surface contact is zero
u=0
so from the equation
u = 0.81 + 9.2y + (4.1 × 10³y³)
at y = 0
u = 0.81 + 9.2(0) + (4.1 × 10³(0)³)
u = 0.81 ft/s
The velocity according to the above equation at y=0 is 0.81 ft/sec but since the fluid is flowing on flat surface which is stationary this value is wrong hence the equation is NOT CORRECT
