My question is about a toy hovercraft - a balloon connected to a CD. I need to know about something. How does cross section of the pipe affect the time that the toy hovercraft hovers above the surface?
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$\begingroup$ Have you looked at any of the links in my earlier answers/ comments? They contain the equations you need. Find them, and see what you can learn from them. Then ask for more help when you are still stuck. By the way - nice diagram. $\endgroup$– FlorisMar 15, 2015 at 18:36
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$\begingroup$ Which ones? can you show them to me please? $\endgroup$– David 2000Mar 15, 2015 at 18:37
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$\begingroup$ The comment with the link was physics.stackexchange.com/questions/170556/… $\endgroup$– FlorisMar 15, 2015 at 18:42
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$\begingroup$ And more at hyperphysics.phy-astr.gsu.edu/hbase/hframe.html $\endgroup$– FlorisMar 15, 2015 at 18:44
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$\begingroup$ Sir I studied the all but I didn't find the answer of my new question. The effect of cross section on the time. I mean for example what will happen if we cover half of the pipe ( cross section ). $\endgroup$– David 2000Mar 15, 2015 at 18:48
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1 Answer
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The exact answer to your question can be found at http://hyperphysics.phy-astr.gsu.edu/hbase/ppois2.html#tub
There it shows that the flow rate goes as the 4th power of the radius of a pipe - so if you double the diameter, air will flow 16x faster.
The reason behind this is something I described in some detail in this earlier answer.
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$\begingroup$ OK sir, but what about the time. You proved that air flows 16x faster but air goes through a smaller area. How about the time? What would the relation of the r ( of the pipe ) and the time that hovercraft hovers? $\endgroup$ Mar 16, 2015 at 13:38
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$\begingroup$ If the air flows 16x more slowly, it will take 16x longer for the same volume of air to escape, assuming that the air flow is still sufficient for hovering - which depends on how snug the fit is between your disk and the table. $\endgroup$– FlorisMar 16, 2015 at 13:42