At the bend in a pipe, along the outside curve, the pressure A. decreases. B. can’t change. C. increases. At the bend in a pipe, along the outside curve, the water’s speed A. decreases. B. can’t change. C. increases.

Water slows down and backs up against the outside wall. The streamline broadens to show this.

At the bend in a pipe, along the inside curve, the pressure A. decreases. B. can’t change. C. increases. Viscosity may make the fluid “cling” to the inside wall of the pipe and try to follow the curve… At the bend in a pipe, along the inside curve, the water’s speed A. decreases. B. can’t change. C. increases.

Water slows down and backs up against the outside wall. The streamline broadens to show this. Water speeds up and races ahead along the inside wall. Streamlines thin to show this! Stream- lines regain their more even distri- bution along straight sections of pipe.

Water slows down and backs up against the outside wall. Water speeds up and races ahead along the inside wall. Constant “energy/volume” Bernoulli’s principle argues that the fluid pressure must be A. greater along the inside of the curve. B. greater along the outside of the curve. C. exactly the same along inside and outside.

Inside curve Outside curve The pressure gradient points (from region of highest pressure toward region of lowest pressure) A. to the right.B. to the left. C. into the screen (away from you). D. toward the center of curvature.

Inside curve Outside curve Notice the pressure gradient forces fluid toward the center of its curved path…providing the centripetal force that ANY mass needs to turn a corner!

Consider an obstacle in an airstream: (or an object moving through the air) If there air is traveling rapidly enough Its easy to imagine an empty “airpocket” created in the obstacle’s “shadow.”

On the windward side of this obstacle we expect the pressure to be: A. high, and the air speed to slow down. B. high, where the air speed increases. C. low, with the air speed slowing down. D. low, where the air speed increases.

On the windward side of the obstacle we expect the streamlines here to A. broaden. B. stay uniform in their spacing. C. thin.

Where does this air go?

Builds high pressure deflecting air aside. Air slows, bends away from the barrier wall. Like in a plumbing elbow, high pressure forms at the outside of the bend. As dry leaves that before the wild hurricane fly, When they meet with an obstacle, mount to the sky,

Currents curve over the corners to rejoining the airstream. The air pressure at these corners must be A. even higher than felt by the side facing the wind. B. equal to the surrounding atmospheric pressure. C. lower than the surrounding atmospheric pressure. D. zero.

On the leeward side we might expect currents to be pretty still. …curve around the corner, spill over the sides. Viscosity may force the closest layers to creep along the surface to which they stick…

On the leeward side we might expect currents to be pretty still. Viscosity may force closest layers to creep along the surface to which they stick and curve around the corner, spill over the sides.

Streamlines like this are also used to describe the flow moving past & around objects moving through the fluid! Expect high pressure again where rushing air currents meet. If moves FAST ENOUGH punches an air pocket behind it… air will rush in to fill this vacuum! How rapidly this air closes in the space behind determines the size of the “wake” of “dead air.”

If relative motion between fluid and object is SMALL smooth laminar flow results: Amazingly, there are no pressure differences retarding motion! Only viscous drag slows things down (a friction-like effect).

But we ABSOLUTELY expect that at high speeds a wake does indeed develop! This leaves a wake outlined by “turbulence”. Conservation of angular momentum can force this air that comes spinning around the corners to develop vortices!

Which air foil design do Indy race cars have fixed on the back to aid in cornering? AB For greater cornering, more friction is needed to prevent skidding in the curve. Since f =  N, friction is increased with a greater normal force. That requires pushing down on the car. The airfoil in B has lower pressure on the underside, creating a pressure force down. C

Your hand stuck out the window into the airstream around a moving car palm forward builds high pressure on your windward palm with a lower pressure trailing wake. You experience a pressure drag that drives your hand BACKWARD.

A hand tipped slightly upward may actually be pushed up! (the faster rushing air across the bottom surface produces lower pressure!) A hand tipped slightly downward can actually be pushed down!

But how SLOWLY must flow be for the streamlines to remain laminar? At what speeds does turbulence develop? Let’s try to imagine what factors might influence the onset of turbulence… What might enhance formation of air pockets? What might enhance air filling in such pockets?

Speed: Faster objects should produce A. larger wakes, more turbulence. B. smaller wakes, less turbulence. C. no noticeable difference in wake or turbulence. Fluid density: Denser fluids should produce Viscosity: More viscous fluids should produce Size of obstacle: Larger objects should produce

Osborne Reynolds (1842 – 1912) Considering these same variables, Reynolds defined a predictor ( formed basically by just multiplying them all together ): Reynolds number density · obstacle size · speed = viscosity < 2000Laminar flow > 2000Turbulent flow

Low pressure High speed Viscous drag (air friction) does affect this ball traveling with laminar flow through the air. But NO pressure drag!

Reynolds number density · obstacle size · speed = viscosity  air = kg/m 3 at sea level and 20 o C D basball = 2.9 inches = 0.07 m  air = kg/(m·sec) v v Maximum v  50 cm/sec Above that turbulence sets in.

to keep the closest layers riding the surface At high speeds viscosity is not enough especially considering the high pressure that has developed there! down the back side of the ball. The surface layers of air sheer away from the surface!

Now the ball definitely suffers a PRESSURE DRAG!

SOME ANSWERS Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9 Question 10 Question 11 Question 12 C. increases. A. decreases. Water is being forced into a constricted space. Higher pressure slows it as it enters the bend. C. increases. A. decreases. Water clinging to the inside surface of the pipe is forced away from the pipe’s center, giving subsequent layers of water more room to flow. When water encounters a new region of lower pressure it rushes in…speeds up! B. along the outside. Since, constant, wherever the speed is low, the pressure will be high. D. toward the center. Providing the centripetal force that guides the water into a turn. A. high, & air speed to slow.Air is blocked and flow backs up! The lower pressure on the underside, creates a pressure force down, increasing the frictional force. B A. B. Speed: Density: Viscosity: Size: Greater fluid speed or density, increases the fluid’s momentum…and inertia would tend to keeping it moving in as straight a path as possible. This would be more likely to create the “air pocket” or shadow behind. An increase in viscosity would make the fluid to stick more to surfaces, riding down the backside of the object, more effectively closing the gap otherwise left behind,