Chapter 1 FLUID PROPERTIES. The engineering science of fluid mechanics: fluid properties, the application of the basic laws of mechanics and thermodynamics, and orderly experimentation.
Figure 1.1 Deformation resulting from application of constant shear force.
A substance is placed between two closely spaced parallel plates so large that conditions at their edges may be neglected. The lower plate is fixed, and a force F is applied to the upper plate, which exerts a shear stress F/A on any substance between the plates. A is the area of the upper plate. When the force F causes the upper plate to move with a steady (nonzero) velocity, no matter how small the magnitude of F, one may conclude that the substance between the two plates is a fluid.
μ is the proportionality factor and includes the effect of the particular fluid
- Newton's law of viscosity
- proportionality factor μ: viscosity of the fluid
Model illustrating transfer of momentum.
and inserting dimensions F, L, T for force, length, and time,
shows that μ has the dimensions FL-2T.
- occurs in many applications (e.g., in the dimensionless Reynolds number for motion of a body through a fluid, Vl/ν, in which V is the body velocity and l is a representative linear measure or the body size)
A liquid has a viscosity or 0.005 Pa·s and a density or 850 kg/m3. Calculate the kinematic viscosity:
In Fig. 1.4 the rod slides inside a concentric sleeve with a reciprocating motion due to the uniform motion of the crank. The clearance is δ and the viscosity μ. Write a program in BASIC to determine the average energy loss per unit time in the sleeve. D = 0.8 in, L = 8.0 in, δ = 0.001 in, R = 2 ft, r = 0.5 ft, μ = 0.0001 lb s/ft2, and the rotation speed is 1200 rpm.
The energy loss in the sleeve in one rotation is the product of resisting viscous (shear) force times displacement integrated over the period of the motion. The period T is 2π/w, where w = dθ/dt. The sleeve force depends upon the velocity. The force Fi and position xi are found for 2n equal increments of the period. Then by the trapezoidal rule the work done over the half period is found
Using the law of sines to eliminate φ, we get
Figure 1.5 lists the program, in which the variable RR represents the crank radius r.
and that has constant specific heats. P is the absolute pressure; vs is the specific volume; R is the gas constant; T is the absolute temperature.
knowledge of relative molecular mass leads to the value of R
A gas with relative molecular mass of 44 is at a pressure or 0.9 MPa and a temperature of 20oC. Determine its density.
Then, from Eq.(1.6.2)
A liquid compressed in a cylinder has a volume of 1 L (1000cm3) at 1 MN/m2 and volume of 995 cm3 at 2 MN/n2. What is its bulk modulus of elasticity?
Table 1.2 Approximate properties of common liquids at 20oC and standard atmospheric pressure