Indian Institute of Space Science and Technology, Thiruvananthapuram
Department of Aerospace Engineering
AE213 FLUID MECHANICS : ASSIGNMENT – 1
Date of submission : 12 August 2016
1. A rigid container is partially filled with a liquid at 1.5 MPa. The volume of liquid is 1.232 L.
At a pressure of 3.0 MPa, the volume of liquid is 1.231 L. Find the average bulk modulus of
elasticity of the liquid over the given range pressure if the temperature after compression is
allowed to return to its initial value. What is the coefficient of compressibility, β ?
2. Often the assumption is made that the flow of a certain fluid can be considered as incompressible
flow if the density of the fluid changes by less than 2%. If air is flowing through a tube such
that the air pressure at one section is 62.0 kPa and at a downstream section it is 59.3 kPa at
the same temperature, do you think that this flow could be considered an incompressible flow?
Support your answer with the necessary calculations. Assume standard atmospheric pressure.
3. Magnet wire is to be coated with varnish for insulation by drawing it through a circular die
of 0.9 mm diameter. The wire diameter is 0.8 mm and it is centered in the die. The varnish
(µ = 20 × 10−3 Pas) completely fills the space between the wire and the die for a length of
20 mm. The wire is drawn through the die at a speed of 50 m/s. Determine the force required
to pull the wire.
4. The space between two 15 cm -long concentric cylinders is filled with glycerin (ν = 1180 cSt).
The inner cylinder has a radius of 7.5 cm and the gap width between cylinders is 2.5 mm.
Determine the torque and the power required to rotate the inner cylinder at 180 rev/min. The
outer cylinder is fixed. Assume the velocity distribution in the gap to be linear.
5. A block of weight W slides down an inclined plane while lubricated by a thin film of oil, as
in figure below. The film contact area is A and its thickness is h. Assuming a linear velocity
distribution in the film, derive an expression for the ”terminal” (zero-acceleration) velocity V
of the block.
6. A thin plate is separated from two fixed plates by very viscous liquids µ1 and µ2 , respectively,
as in figure below. The plate spacings h1 and h2 are unequal, as shown. The contact area is
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A between the center plate and each fluid. (a) Assuming a linear velocity distribution in each
fluid, derive the force F required to pull the plate at velocity V . (b) Is there a necessary relation
between the two viscosities, µ1 and µ2 ?
7. A uniform film of oil 0.13 mm thick separates two discs, each of 200 mm diameter, mounted
co-axially. Ignoring edge effects, calculate the torque necessary to rotate one disc relative to
the other at a speed of 44 rad/s (7 rev/s) if the oil has a dynamic viscosity of 0.14 Pas.
8. A shaft of 70 mm is being pushed at a speed of 400 mm/s through a bearing sleeve of 70.2 mm
diameter and 250 mm long. The clearance, assumed uniform, is filled with oil at 20o C with
ν = 0.005m2 /s and specific gravity 0.9. Find the force exerted by the oil on the shaft.
9. A small circular jet of mercury 200 µm in diameter issues from an opening. What is the pressure
difference between the inside and outside of the jet at 20o C ?
10. A clean wire is bent into a U–shaped frame. The legs of the U are separated by 20 mm. A
straight wire is held in place perpendicular to the legs of the U, and the assembly is dipped into
a container of glycerine at 20o C. After the assembly is removed from the glycerine, a film is
seen to be attached to the interior of the assembly. What force is required to hold the straight
wire in place?
11. Under the right conditions, it is possible, due to surface tension, to have metal objects float on
water. Consider placing a short length of a small diameter steel (specific weight = 76 kN/m3 )
rod on a surface of water. What is the maximum diameter that the rod can have before it will
sink? Assume that the surface tension forces act vertically upward. Note: A standard paper
clip has a diameter of 0.9 mm. Partially unfold a paper clip and see if you can get it to float
on water. Do the results of this experiment support your analysis?
12. Some non-Newtonian fluids behave as a Bingham plastic for which shear stress can be expressed
as τ = τy + µ du
dr . For the flow of Bingham plastic in a horizontal pipe of radius R, the velocity
τ
∆p 2
profile is given as u(r) = 4µL
(r − R2 ) + µy (r − R), where ∆p/L is the constant pressure drop
along the pipe per unit length, µ is the dynamic viscosity, r is the radial distance from the
centerline, and τy is the yield stress of Bingham plastic. Determine (a) the shear stress at the
pipe wall and (b) the drag force (force acting along the direction of main flow) acting on a pipe
section of length L.
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