Warmup 3/1/16 Is it worth anything to learn the Bible in its original languages? To calculate the work involved in pumping fluids pp 398: 2, 3, 4, 5 Objective.

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Presentation transcript:

Warmup 3/1/16 Is it worth anything to learn the Bible in its original languages? To calculate the work involved in pumping fluids pp 398: 2, 3, 4, 5 Objective Tonight’s Homework

Notes on Pumping Fluids Today we revisit a few old concepts fused together. A long time ago, we said… work = force (weight) distance We also said… Weight = density volume We can combine both these concepts when discussing the energy it takes to pump a fluid from a tank.

Notes on Pumping Fluids Example: If the tank at right is full of water, calculate the energy needed to pump all the water out from the top

Notes on Pumping Fluids Example: If the tank at right is full of water, calculate the energy needed to pump all the water out from the top. To solve a problem like this, we need to do a few things: 1) Calculate the volume of each infinitely thin slice. 2) Calculate the weight (or force) each slice has 3) Integrate the thin slices over the entire height of the tank or container

Notes on Pumping Fluids Example: If the tank at right is full of water, calculate the energy needed to pump all the water out from the top. Calculate the volume of each infinitely thin slice: Each slice has a volume of 410dh

Notes on Pumping Fluids Example: If the tank at right is full of water, calculate the energy needed to pump all the water out from the top. Calculate the weight (or force) each slice has: Weight = density volume Weight = (9800)(410dh)

Notes on Pumping Fluids Example: If the tank at right is full of water, calculate the energy needed to pump all the water out from the top. Integrate the thin slices over the entire height of the tank or container: Work = force distance Work = (9800)(410dh) (6 – h) Total work = ∫ (9800)(410dh) (6 – h) Height we’re lifting the liquid to How deep the liquid itself is

Notes on Pumping Fluids Example: If the tank at right is full of water, calculate the energy needed to pump all the water out from the top. Total work = ∫ (9800)(410dh) (6 – h) Total work = ∫ 392,000 (6 – h) dh Total work = 392,000[6h – h 2 /2] = 7,056,000 J

Notes on Pumping Fluids A few things to notice: Unlike our pressure problems, in these, the 3-D depth matters. This is because we’re talking about a total amount of liquid. Another thing to note: If you have a symmetrical tank, you could split it down the middle, do the problem, and double your answer afterwards. Keep this in mind for some of the homework.

Group Practice Look at the example problems on pages 396 through 398. Make sure the examples make sense. Work through them with a friend. Then look at the homework tonight and see if there are any problems you think will be hard. Now is the time to ask a friend or the teacher for help! pp 398: 2, 3, 4, 5

Exit Question Does the length of a tank matter in these problems? a) Yes b) No c) It depends