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course Phy 232
Problem Number 4Water is descending in a vertical pipe of diameter 8 cm. At a certain level the water flows into a smaller pipe of diameter 1.2 cm. At a certain instant the gauge pressure of the water at a point 80 cm above the narrowing point is 86.6 kPa and the water there is moving at 94 cm/s. What is the gauge pressure of the water just above the narrowing point?
What is the pressure change across the narrowing point?
Three points are involved here, the 'known point' 80 cm above, the point just above, and the point just below the narrowing. Number these points 0, 1 and 2. We will apply Bernoulli's Equation to these points, two points at a time..
We're given P0, y0 and v0. So we know the required variables for State 0. We will compare each of the other points to point 0.
At point 1 we know y1 and v1 (v1 = v0). So we easily find `dP and therefore P1.
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I don't understand how we know y1 here. Where did that come from?
@& You can let either point be the 0 point for altitude. So you could let y1 = 0, in which case y2 would be -80 cm.. Or you could let y1 = 80 cm so that y2 is 0.*@
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At point 2 we know y2, from dimensions we can find v2 so again we easily find `dP and therefore P2."
@& Hopefully the note I inserted will clarify this.*@