Solved Problems and Questions on fluid properties

Solved Problems and Questions on fluid properties
The quantities viscosity µ, velocity V, and surface tension Y may be combined into
a dimensionless group. Find the combination which is proportional to µ. This group has a customary name, which begins with C. Can you guess its name?

Solution: The dimensions of these variables are {µ} ??{M/LT}, {V} ??{L/T}, and {Y} ??{M/T2}. We must divide µ??by Y to cancel mass {M}, then work the velocity into the group:
{?/Y}= {(M/LT)/(M/T2)}= {L/T}.
hence multiply by {V}={T/L}
finally obtain Ans:
{(? V)/Y}=dimensionless.
This dimensionless parameter is commonly called the Capillary Number.
2.
Suppose that the fluid being sheared in Fig. 1.1is SAE 30 oil at 20°C. Compute the shear stress in the oil if V = 3 m/s and h = 2 cm.
The shear stress is found from Eq:

From Table for SAE 30 oil, µ = 0.29 kg/(m . s). Then, for the given values of V and h,
Eq. (1) predicts:
?=(0.29kg/m.s*3m/s)/2m=43kg/(m.s2)=43N/m2 =43 Pa
When a vehicle such as an automobile slams on its brakes (locking the wheels) on a very wet road it can “hydroplane.” In these circumstances a film of water is created between the tires and the road. Theoretically, a vehicle could slide a very long way under these conditions though in practice the film is destroyed before such distances are achieved (indeed, tire treads are designed to prevent the persistence of such films). To analyze this situation, consider a vehicle of mass, M, sliding over a horizontal plane covered with a film of liquid of viscosity, ?. Let the area of the film under all four tires be A and the film thickness (assumed uniform) be h.
a. If the velocity of the vehicle at some instant is V, find the force slowing the vehicle down in terms of A, V, h, and ?.
b. Find the distance, L, that the vehicle would slide before coming to rest assuming that A and h remain constant (this is not, of course, very realistic).
c. What is this distance, L, for a 1000 kg vehicle if A = 0.1 m2 , h = 0.1 mm, V = 10 m/s, and the water viscosity is ??= 0.001 kg/(m?s)?

sol:
?=F/A= ?V/h
?F= ?V/h A
L= (MhV_o)/?A
L= 10,000 m


The specific weight of water at ordinary pressure and temperature is 62.4 lb/ft3 . The specific gravity of mercury is 13.56. Compute the density of water and the specific weight and density of mercury.
Solution:
?water=?water/g=1.938 slugs/?ft?^3

?mercury=S.G.mercury*?water=846 lb/?ft?^3

?mercury=S.G.mercury*?water=26.3 slugs/?ft?^3
The specific weight of water at ordinary pressure and temperature is 9.81 kN/m3 . The specific gravity of mercury is 13.56. Compute the density of water and the specific weight and density of mercury
Sol:
Ans: a. 1000kg/m3
b. 133.0 kN/m3