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Physics 7B DLM 11 Overview
Model/Approach: Energy Density Model
Finish 6.1.3 (~15 min) Act-6.1.4 Wrap-up of DLM 10 FNTs 1 - 7 (~ 60 min) Learning Goals:
- Get a firmer grasp on the meaning and behavior of the various fluid parameters in various kinds of flow phenomena.
- Get a firmer grasp on how to use the energy density model to analyze fluid phenomena without flow.
- Get a firmer grasp on how to use the energy density model to analyze fluid phenomena with flow. AC-6.1.5 Analyzing A Fluid Circuit (~ 20 min) Learning Goals
- Gain experience analyzing the fluid circuit. - Gain further experience working with the extended energy density model (including dissipation and energy sources/pumps)
Announcements
- Reading Assignment - Read Unit 6 through page 78.
Physics 7B Activity 6.1.4 DLM 11
Wrap-up of DLM 10 FNTs 1 - 7
In Your Small Group
FNTs 2 and 3 (10 mins.) Compare your responses to these two FNTs with other members of your small group. If you have any remaining questions, put only these questions on the board. Quick whole class discussion FNTs 1, 4, and 5 (25 mins.) Your DL instructor will tell you which one of these FNTs to put on the board. Quickly compare your response to the assigned FNT with other group members and put it on the board. Quick whole class discussion FNT 6 (5 mins.) Discuss your responses to this FNT in your small group. Nothing to put on board. How does the sudden enlargement of the artery affect the pressure of the blood at that point, and how does that change in pressure then affect the enlarged artery? When blood flows from the arteries into the capillaries, it goes from one large "tube" to several much smaller ones. It is well known that the blood slows down when it reaches the capillaries (a good thing, since the slower rate improves the oxygen and CO 2 exchange between the blood and the tissues surrounding the capillaries). According to our energy density model, fluids speed up when the tube is narrowed. How then can we explain why blood slows down when it enters the capillaries? The explanation here does not have anything to do with dissipation. Quick whole class discussion FNT 7 (20 mins.) In order to apply the energy density model to a pair of points, those points must be contained in a fluid system that is continuous and “doing the same thing” all along the fluid.
- Identify the four separate fluid systems in this physical situation.
- In which fluid system(s) can we assume gravitational potential energy density changes are negligible?
- In which fluid system(s) can we assume all energy density changes are negligible? How does this simplify the analysis of this physical situation? That is, which fluid system(s) must we actually apply the transport equation to? Sketch the horizontal pipe and u-tube on the board, and label the two pairs of points that you need to apply the energy density model to, in order to determine the difference in height of water in the u-tube. Write on the board only the appropriate form of the equation expressing energy conservation for each of the two pairs of points. Include subscripts in your equations. Be prepared to explain how the terms in your equation are correlated with the points in your sketch. Don’t put all your algebra and numerical answers on the board. Compare your numerical answers with others in your group and correct any mistakes you made. Don’t put numerical answers on the board. Whole Class Discussion
Physics 7B Exit Handout DLM 11 FNTs: Use the fluid transport equation (fully extended Bernoulli equation) to logically respond to these FNT prompts. These FNTs were used previously as quiz questions; you should by now be able to apply the energy density model, using the fluid transport equation, to respond to the prompts. FNT 1. Three identical garden hoses (same length and same inner diameter) are attached to the same faucet through a three-way divider, which supplies water at the same pressure to all three hoses. All three hoses are open to the atmosphere at their other ends. Hose A runs along a level path at the elevation of the faucet. Hose B runs down a hill and its free end is some 10 ft below the level of the faucet. Hose C runs up and over a high wall, but its free end is back at the elevation of the faucet. How do the flow rates through the three hoses compare? Justify your answer using the physics we have studied this quarter. Make certain to explicitly show the pair of points you are applying the model between, and this should be your first step in solving these problems. FNT 2 Water flows through a horizontal pipe similar to the pipe in DL. It enters the pipe at point (1), then leaves the pipe at point (2), which is open to the atmosphere. The height of the water in each vertical column is shown at right. Now suppose that the length of this pipe is doubled. The pressure at point (1) is the same as before. Point (2) is still open to the atmosphere. Water is again allowed to flow from point (1) to point (2). (a) We find the flow rate in the longer pipe is smaller than the flow rate in the shorter pipe. Explain why this happens. By what factor would the flow of water through this pipe decrease? Explain your answer and show your reasoning. (b) Fill in the water levels in each of the vertical tubes in the pipe whose length has been doubled, in the diagram above. Be clear and accurate in drawing each water level. Side View showing elevations A B C 1 flow 2 open to air 1 flow 2 open to air
