fundamentals of engineering supplied-reference handbook - Ventech!

The Field Equation is derived when the energy equation is
applied to one-dimensional flows.
Assuming no friction losses and that no pump or turbine
exists between sections 1 and 2 in the system,
p
γ
2
2
2
V
+ + z
2g
2
2
1
p1
V
= + + z1
, where
γ 2g
p1, p2 = pressure at sections 1 and 2,
V1, V2 = average velocity of the fluid at the sections,
z1, z2 = the vertical distance from a datum to the sections
(the potential energy),
γ = the specific weight of the fluid (ρg), and
g = the acceleration of gravity.
FLUID FLOW
The velocity distribution for laminar flow in circular tubes
or between planes is
⎡ 2
⎛ r ⎞ ⎤
v = vmax
⎢1
− ⎜ ⎟ ⎥ , where
⎢⎣
⎝ R ⎠ ⎥⎦
r = the distance (m) from the centerline,
R = the radius (m) of the tube or half the distance
between the parallel planes,
v = the local velocity (m/s) at r, and
vmax = the velocity (m/s) at the centerline of the duct.
vmax = 1.18V, for fully turbulent flow
(Re > 10,000)
vmax = 2V, for circular tubes in laminar flow and
vmax = 1.5V, for parallel planes in laminar flow, where
V = the average velocity (m/s) in the duct.
The shear stress distribution is
τ
τ
w
=
r
R
, where
τ and τw are the shear stresses at radii r and R respectively.
46
FLUID MECHANICS (continued)
The drag force FD on objects immersed in a large body of
flowing fluid or objects moving through a stagnant fluid is
2 A
CDρV
FD
= , where
2
CD = the drag coefficient (see page 55),
V = the velocity (m/s) of the undisturbed fluid, and
A = the projected area (m 2 ) of blunt objects such as
spheres, ellipsoids, disks, and plates, cylinders,
ellipses, and air foils with axes perpendicular to the
flow.
For flat plates placed parallel with the flow
CD = 1.33/Re 0.5 (10 4 < Re < 5 × 10 5 )
CD = 0.031/Re 1/7 (10 6 < Re < 10 9 )
The characteristic length in the Reynolds Number (Re) is
the length of the plate parallel with the flow. For blunt
objects, the characteristic length is the largest linear
dimension (diameter of cylinder, sphere, disk, etc.) which is
perpendicular to the flow.
AERODYNAMICS
Airfoil Theory
The lift force on an airfoil is given by
2
CLρV AP
FL
=
2
CL = the lift coefficient
V = velocity (m/s) of the undisturbed fluid and
AP = the projected area of the airfoil as seen from above
(plan area). This same area is used in defining the drag
coefficient for an airfoil.
The lift coefficient can be approximated by the equation
CL = 2πk1sin( α+β ) which is valid for small values of
α and β .
k1 = a constant of proportionality
α = angle of attack (angle between chord of airfoil and
direction of flow)
β = negative of angle of attack for zero lift.
The drag coefficient may be approximated by
2
L
C
CD = CD∞+
πAR
CD∞ = infinite span drag coefficient
2
b Ap
AR = =
A 2
c
p