Sheet #1

Fluid properties

1. Review problems ( Density, Specific Gravity, Dimensions, Dimensional

Homogeneity, and Units):

What is the difference between intensive and extensive properties?

What is specific gravity? How is it related to density?

A 100-L container is filled with 1 kg of air at a temperature of 27°C.

What is the pressure in the container?

A mass of 0.5-kg of argon is maintained at 1400 kPa and 40°C in a

tank. What is the volume of the tank?

A fluid that occupies a volume of 32 L weighs 280 N at a location

where the gravitational acceleration is 9.80 m/s2. Determine the mass

of this fluid and its density.

The air in an automobile tire with a volume of 0.015 m3 is at 30°C and

140 kPa. Determine the amount of air that must be added to raise the

pressure to the recommended value of 210 kPa. Assume the

atmospheric pressure to be 100 kPa and the temperature and the

volume to remain constant.

Verify the dimensions, in the MLT system, of the following quantities:

(a) frequency, (b) stress, (c) torque, and (d) work.

The force, F, of the wind blowing against a building is given by,

where V is the wind speed, the density of the air, A the cross-sectional

area of the building, and CD is a constant termed the drag coefficient.

Determine the dimensions of the drag coefficient.

A formula to estimate the volume rate of flow, Q, flowing over a dam

of length, B, is given by the equation

Where H is the depth of the water above the top of the dam 1called the

head2. This formula gives Q in ft3/s when B and H are in feet. Is the

constant, 3.09, dimensionless? Would this equation be valid if units

other than feet and seconds were used?

2. What pressure must be applied to water ( ) to reduce its

volume by ?

3. The bulk modulus of elasticity K is defined by

show that it is

equivalent to

where the pressure, is the density and is the

volume.

4. Eight kilometers below the surface of the ocean, the pressure is

Determine the specific weight of the sea water at this depth if the specific weight at

the surface is 3 and the average bulk’s modulus of elasticity is

Assume that does not change significantly.

5. Calculate the velocity of sound in water at ,( ).

6. Calculate the velocity of sound in air at o , abs .

7. A car tire is filled with air at a gage pressure of 2 inside a garage at

o, what will be the pressure in the tire at: a) o

& b) o assume no

change in the volume of the tire also a standard atmospheric pressure

of .

8. A thin plate moves between two parallel, horizontal flat surfaces at a constant

velocity of . The two surfaces are spaced apart, the plate is apart

from the top surface and the medium between them is filled with oil whose

viscosity is the part of the plate immersed in oil at any given time is

long and wide. If the plate moves between the surfaces. Determine the

force required to maintain this motion if

(a) Both upper and lower surfaces are stationary.

(b) The upper surface moves at velocity = in the same direction as plate

where the lower surface remains stationary.

8. Fluid flow through a circular pipe is one-dimensional, and the velocity profile for

Laminar flow is given by max

, where is the radius of the pipe,

is the radial distance from the center of the pipe, and max is the maximum flow

velocity, which occurs at the center, given that , max and

Determine: (a) The shearing stress acting on the pipe wall.

(b) The shearing stress acting on a plane parallel to the pipe walls

And passing through the centerline (mid-plane).

(c) Given the pipe length , calculate the drag force applied by

The fluid on pipe.

9. Through a very narrow gap of height , a thin plate of very large extent is

being pulled at constant velocity . on one side of the plate the oil viscosity is

while on the other side the oil viscosity is as shown in the next figure,

Calculate the position of the plate so that the drag force on it will be minimum.

10. A -diameter shaft is pulled through a cylindrical bearing as shown in the

figure. The lubricant that fills the gap between the shaft and bearing is an

oil having a kinematic viscosity of and a specific gravity of

Determine the force required to pull the shaft at a velocity of Assume the

velocity distribution in the gap is linear.

11. The viscosity of a fluid is to be measured by a viscometer constructed of two

long concentric cylinders as shown in the figure.The outer diameter of the

inner cylinder is , and the gap between the two cylinders is .

The inner cylinder is rotated at , and the torque is measured to be N.m,

Determine the viscosity of the fluid.

12. Oil of viscosity fills the gap which is very small, calculate the torque

required to rotate the cone at constant speed .

13. In some damping systems, a circular disk immersed in oil is used as a damper,

as shown in Figure. Show that the damping torque is proportional to angular speed

in accordance with the relation,

Where C equal to,

Assume linear velocity profiles on both sides of the disk and neglect the tip effects.

14. The clutch system shown in Figure is used to transmit torque through a 2-mm-

thick oil film with μ= 0.38 N.s/m2 between two identical 30-cm-diameter disks.

When the driving shaft rotates at a speed of 1450 rpm, the driven shaft is observed

to rotate at 1398 rpm. Assuming a linear velocity profile for the oil film, determine

the transmitted torque.