Chem 2O04 Fluid MechanicsAssignment 1
a) Since we know that the friction factor is dimensionless, we know that the other side of the
equation must also be dimensionless. Since the only variable on the right side of the equation are
ε (relative roughness) and Re (Reynolds number), they must both be dimensionless.
Figure : Plot of Log f vs. Log Re(Range of 100000-5000000)
The different ε relative roughness results in a different starting spots and a steeper curvature,
where the lower the ε, the more steep the curve.
b) Starting with the equation F = μA y relating the force with density, area, speed and height.
We then replace u and y, to get F = μA l . Then since T = r X F, and μ is uniform along the
T = (R 0 R)iμA l .
Question 3: a)
b) When the ball is completely submerged, the forces acting on it include T(tension), F g
(gravity), F (water), F (carbcn tetrachloride) and F (buoyancy). bince we know the ball is not
accelerating, ∑F = ma, a=0 so ∑F = 0. Thus, 0 = T + F + F +F +F . Using thewconvectionbof
up as positive, we can rewrite the force equation as T = F + F +F - F .
g w c b
Expanding this out we get: T = (SG x ρ x V x g)+ (h x ρ x g) + (h *x SG x ρ x g) –
steel ref steel w w