Lift Drag Fluid Flow

Overview

Engineering reference data for Lift Drag Fluid Flow in fluid mechanics.

Key Formulas

Reynolds Number

$Re = \frac{\rho v D}{\mu}$

Ratio of inertial to viscous forces — determines flow regime.

Bernoulli's Equation

$P + \frac{1}{2}\rho v^2 + \rho g h = \text{const}$

Conservation of energy for steady, inviscid, incompressible flow.

Continuity Equation

$A_1 v_1 = A_2 v_2$

Conservation of mass for incompressible flow.

Darcy-Weisbach

$\Delta P = f \frac{L}{D} \frac{\rho v^2}{2}$

Pressure drop due to friction in a pipe.

Variables

Symbol	Description	Unit
$Re$	Reynolds number	—
$\rho$	Fluid density	kg/m³
$v$	Flow velocity	m/s
$D$	Characteristic dimension	m
$\mu$	Dynamic viscosity	Pa·s
$P$	Pressure	Pa
$f$	Darcy friction factor	—

Worked Example: Aircraft Aerodynamics

The following example illustrates the application of the lift, drag, and power equations for an aircraft wing.

Given Parameters:

• Velocity, $v = 100 \text{ m/s}$
• Wing Area, $A = 20 \text{ m}^2$
• Drag Coefficient, $c_D = 0.06$
• Lift Coefficient, $c_L = 0.7$
• Air Density, $\rho = 1.2 \text{ kg/m}^3$

Calculations:

1. Lifting Force ($F_L$): Using the lift equation:

$$F_L = c_L \cdot \frac{1}{2} \rho v^2 A$$

Substituting the values:

$$F_L = 0.7 \cdot \frac{1}{2} \cdot (1.2 \text{ kg/m}^3) \cdot (100 \text{ m/s})^2 \cdot (20 \text{ m}^2) = 84,000 \text{ N} = 84 \text{ kN}$$

2. Drag Force ($F_D$): Using the drag equation:

$$F_D = c_D \cdot \frac{1}{2} \rho v^2 A$$

Substituting the values:

$$F_D = 0.06 \cdot \frac{1}{2} \cdot (1.2 \text{ kg/m}^3) \cdot (100 \text{ m/s})^2 \cdot (20 \text{ m}^2) = 7,200 \text{ N} = 7.2 \text{ kN}$$

3. Required Thrust Power ($P$): The power required to overcome drag is the product of drag force and velocity.

$$P = F_D \cdot v$$

Substituting the values:

$$P = (7,200 \text{ N}) \cdot (100 \text{ m/s}) = 720,000 \text{ W} = 720 \text{ kW}$$

References

• Original Source