1. Fluid Resistance

2. Objectives Define drag
Explain the difference between laminar and turbulent flow.
Explain the difference between frictional drag and pressure drag.
Define viscosity and explain how it can be measured.
Use Stoke’s law and Poiseuille’s Law to solve problems involving fluid resistance.

3. Review
Frictional force – the opposing force resulting when one solid slides against another.
Drag – the opposing force of an object in a fluid.

4. Factors effecting drag
Speed of the object (or fluid)
Size and shape of the object
The physical properties of the fluid

5. Speed of Fluid Laminar (streamlined) - results in frictional drag.
Turbulent – results in pressure drag

6. Speed of Fluid
Drag forces increase linearly with velocity until turbulence takes place.

7. Viscosity ( - eta)  = A v
The property of fluid that describes its internal frictional forces (like the density of a fluid).
Syrup and tar have high viscosity whereas air and water have less viscosity
Viscosity units lb N s s * *
ft2 m2
F y
(Pa • s)
(psi • s)
 =
A v

8. Viscosity (cont.)
A Liquid's viscosity decreases with temperature increase
A Gas’ viscosity increases with increases in temperature
Motor oil rated by the Society of Automotive Engineers (SAE) – SAE10 has less viscosity than SAE 40. What does 10W40 mean?

9. Fdrag = 6 r v  Stokes’ Law
The drag force on an object in fluid flow (or an object moving in a fluid).
Fdrag = 6 r v 
Viscosity
Product of a constant (sphere)
Radius
Speed

10. Terminal Velocity
The constant speed that occurs when the drag force equals the gravitational force acting on an object.

11. Change in pressure for length ‘L’
Poiseuille’s Law
Gives the volume flow rate of a fluid flowing through a tube or pipe.
Pipe radius •
 r 4 P
Change in pressure for length ‘L’
V = -
8  L
Volume flow rate
Viscosity of fluid

12. Factors effecting flow through a Pipe
Radius (cross-sectional area) of pipe
Length of pipe
Viscosity of fluid
Bends or “T’s” in the pipe
-  P
R = • V

13. Summary
Drag is the force that opposes the motion of an object moving through a fluid or the force a moving fluid exerts on a stationary object.
Laminar flow is slow, smooth flow over a surface, where particles follow streamlines. The streamlines define theoretical layers of fluid that do not mix. The friction between the successive layers of fluid is called frictional drag.
Turbulent flow is irregular flow with eddies and whorls that mix the fluid. Turbulence causes a wake behind a moving object. The pressure difference between the fluid outside the wake and the fluid inside the wake causes pressure drag.

14. Summary (cont.)
Drag increases with speed. When turbulence is created, pressure drag increases more rapidly than friction drag.
Viscosity is the property of a fluid that describes its internal friction. The SI units of viscosity are Pa • s.
Stokes’ law can be used to calculate the drag force on a sphere moving at constant speed in a viscous fluid.
When drag equals the gravitational force acting on a falling body, the body falls at a constant speed, called the terminal speed of the body.
Poiseuille’s law can be used to calculate the volume flow rate of pressure drop of viscous fluid flowing through a tube or pipe.