Bernoulli’s Principle Lecturer: Professor Stephen T. Thornton

A sitting person’s blood pressure is measured on the arm, at approximately the same level as the heart. How would the results differ if the measurement were made on the person’s leg instead? A) blood pressure would be lower B) blood pressure would not change C) blood pressure would be higher D) not enough information given to determine Reading Quiz

A sitting person’s blood pressure is measured on the arm, at approximately the same level as the heart. How would the results differ if the measurement were made on the person’s leg instead? A) blood pressure would be lower B) blood pressure would not change C) blood pressure would be higher D) not enough information given to determine. Assuming that the flow speed of the blood does not change, then Bernoulli’s equation indicates that at a lower height, the pressure will be greater. Reading Quiz

Last Time Pascal’s Principle Buoyancy Archimedes Principle Mass flow – equation of continuity

Today Bernoulli equation/principle Applications of Bernoulli principle Read all remaining sections of chapter

Conceptual Quiz A) one-quarter B) one-half C) the same D) double E) four times Water flows through a 1-cm diameter pipe connected to a -cm diameter pipe. Compared to the speed of the water in the 1-cm pipe, the speed in the -cm pipe is higher (or lower) by

A  r 2 radius is reduced byone-half area is reduced by one-quarterspeed must increase by four times(A  v) The area of the small pipe is less, so we know that the water will flow faster there. Because A  r 2, when the radius is reduced by one-half, the area is reduced by one-quarter, so the speed must increase by four times to keep the flow rate (A  v) constant. Conceptual Quiz A) one-quarter B) one-half C) the same D) double E) four times Water flows through a 1-cm diameter pipe connected to a -cm diameter pipe. Compared to the speed of the water in the 1-cm pipe, the speed in the -cm pipe is higher (or lower) by v1v1 v2v2

Bernoulli’s Equation (or Principle) It is basically a conservation of energy. Was derived using work-energy theorem. Works for fluids (gases and liquids). We ignore friction.

Bernoulli’s equation, first version At constant height, h 1 = h 2, This may seem odd, because it says “as the pressure increases, the speed decreases” within the fluid. Remember high v, low P and vice versa!!

Answer: A A 1 v 1 = A 2 v 2 High v, low P.

Conceptual Quiz: Blood flows through a coronary artery that is partially blocked by deposits of plaque along the artery wall. Through what part of the artery is the volume flow of blood the largest? A)The narrow part. B)The wide part before the deposits. C)The wide part after the deposits. D)The volume flow is the same in all parts. Before After

Answer: D The volume and mass flow must not change throughout or else blood would pile up somewhere along the artery.

Conceptual Quiz: The pressure in which part of the coronary artery is the least? A)The narrow part. B)The wide part before the deposits. C)The wide part after the deposits. D)The pressure is the same in all parts. Before After

Answer: A The pressure will be least where the speed is the greatest. That will be in the narrow part of the artery. Before After

The Bernoulli Effect on a Sheet of Paper

Wings are designed to cause air to flow faster over top of the wing. Causes pressure differential resulting in lift. True for birds and airplane wings, but not the whole story!

Force on a Roof Due to Wind Speed Roof might blow off during hurricane!

Air Circulation in a Prairie Dog Burrow Lower P Higher P

An Atomizer – Fast air (low pressure) causes fluid to rise in tube. Do demo

Pitot tube used to measure the speed of airplanes.

Conceptual Quiz: Soft top SUV drives fast. What happens to soft top? A) Soft top bows up. B) Soft top is flat. C) Soft top bows down.

Answer: A Air speed on top is high, so pressure is low. Air speed inside SUV is very low, so pressure is normal. Pressure results in force pushing up. High speed, low pressure.

Do lots of demos (curve ball next slide)

Why does a baseball or softball curve? ball Throw curveballs.

Fluid Emerging from a Hole in a Container See next slide.

Calculate speed of water coming out. Do demo 0

Maximum Height of a Stream of Water

Hurricane.A hurricane-force wind of 200 km/h blows across the face of a storefront window. Estimate the force on the 2.0 m x 3.0 m window due to the difference in air pressure inside and outside the window. Assume the store is airtight so the inside pressure remains at 1.0 atm. (This is why you should not tightly seal a building in preparation for a hurricane).

Fluid Flow Through a Tube

Do toilet paper apparatus demo

Conceptual Quiz An object floats in water with of its volume submerged. When more water is poured on top of the water, the object will: A) have more than ¾ submerged B) stay at the same place C) have less than ¾ submerged D) sink to the bottom E) float up a little

density of the object is of the density of waterso it floats in water We already know that density of the object is of the density of water, so it floats in water (i.e., the buoyant force is greater than its weight). When covered by more water, it must therefore float to the top. Conceptual Quiz A) have more than ¾ submerged B) stay at the same place C) have less than ¾ submerged D) sink to the bottom E) float up a little An object floats in water with of its volume submerged. When more water is poured on top of the water, the object will:

How is the smoke drawn up a chimney affected when there is a horizontal wind blowing outside? A) smoke rises more rapidly in the chimney B) smoke is unaffected by the wind blowing C) smoke rises more slowly in the chimney D) smoke is forced back down the chimney Conceptual Quiz

How is the smoke drawn up a chimney affected when there is a horizontal wind blowing outside? A) smoke rises more rapidly in the chimney B) smoke is unaffected by the wind blowing C) smoke rises more slowly in the chimney D) smoke is forced back down the chimney Due to the speed of the wind at the top of the chimney, there is a relatively lower pressure up there as compared to the bottom. Thus, the smoke is actually drawn up the chimney more rapidly, due to this pressure difference. Conceptual Quiz