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November 18 AP Physics

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In:

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**Objective: To begin our study of fluid dynamics Equation of continuity**

Bernoulli’s equation Success criteria: Be able to use the Bernoulli equation to solve problems.

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**Ideal fluid Fluid is nonviscous Fluid is incompressible**

Fluid motion is steady Fluid moves without turbulence

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**Equation of continuity**

Restatement of conservation of mass

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**A water pipe has a radius of 2 cm and a flow speed of 6 m/s.**

What is the flow rate? What is the flow speed at the nozzle, which has a radius of 1 cm?

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**If the diameter of a pipe increases from 4 cm to 12 cm, what will happen to the flow speed?**

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Bernoulli’s Equation

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**Bernoulli Assumptions**

There are three main variables in the Bernoulli Equation Pressure – Velocity – Elevation To simplify problems, assumptions are often made to eliminate one or more variables Key Assumption # 1 Velocity = 0 Imagine a swimming pool with a small 1 cm hole on the floor of the pool. If you apply the Bernoulli equation at the surface, and at the hole, we assume that the volume exiting through the hole is trivial compared to the total volume of the pool, and therefore the Velocity of a water particle at the surface can be assumed to be zero

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**Bernoulli Assumptions**

Key Assumption # 2 Pressure = 0 Whenever the only pressure acting on a point is the standard atmospheric pressure, then the pressure at that point can be assumed to be zero because every point in the system is subject to that same pressure. Therefore, for any free surface or free jet, pressure at that point can be assumed to be zero.

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**The Continuity Equation**

Bernoulli Assumptions Key Assumption # 3 The Continuity Equation In cases where one or both of the previous assumptions do not apply, then we might need to use the continuity equation to solve the problem A1V1=A2V2 Which satisfies that inflow and outflow are equal at any section

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A pump forces water at a constant flow rate through a pipe with cross sectional area A, gradually decreasing in area to the exit point 1/3 the area. If y=cm and the flow speed of the water just after it leaves the pump is 1m/s, what is the gauge pressure at point 1?

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**An open can is completely filled with water, to a depth of 20. 6 cm**

An open can is completely filled with water, to a depth of 20.6 cm. A hole is punched in the can at a height of 1.7 cm from the bottom of the can. Bernoulli's equation can be used to derive the following formula for the speed of the water flowing from the hole. (a) How fast does the water initially flow out of the hole? (b) How fast does the water flow when the can is half empty?

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**Just substitute the given numbers into Bernoulli's equation. A. h = 0**

Just substitute the given numbers into Bernoulli's equation. A. h = v = sqrt(2*9.81*( )) m/s B. h = v = sqrt(2*9.81*( )) m/s

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**Water flows steadily from an open tank as in the figure below**

Water flows steadily from an open tank as in the figure below. The elevation of point 1 is 10.0m, and the elevation of points 2 and 3 is 2.00m. The cross-sectional area at point 2 is m2; at point 3 it is m2. The area of the tank is very large compared with the cross-sectional area of the pipe.

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Out on overhead

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