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Water pressure problem

  • Thread starter dmk90
  • Start date
  • #1
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Homework Statement


Water flows through a hole at the bottom of a tank that is filled to a height h=3m. The radius of the hole is r1 = 1.5 cm.
1. What is the speed of the water immediately after it leaves the hole?

2. At what distance d below the bottom of the tank is the radius of the stream reduced to r2 = 1 cm?


Homework Equations




The Attempt at a Solution


I managed to solve the speed for 7.7 m/s. However, I'm not sure what formula to use to address the atmospheric pressure that cause the stream to shrink.
 

Answers and Replies

  • #2
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The stream shrinks because it is accelerating gravitationally. As it speeds up, for the flow rate to remain constant, the cross sectional area must decrease.

Chet
 
  • #3
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Based on your clarification, I calculated the velocity at the bottom using the conservation of volumetric flow rate (R = Av = constant), v0 = 17.3. Then g = dv/dt -> dt = dv/g = 0.98 s. Then d = d0 + v0t + 0.5at2 = 12.3, which seems to be the correct result. What do you think?
 
  • #4
19,914
4,092
Based on your clarification, I calculated the velocity at the bottom using the conservation of volumetric flow rate (R = Av = constant), v0 = 17.3. Then g = dv/dt -> dt = dv/g = 0.98 s. Then d = d0 + v0t + 0.5at2 = 12.3, which seems to be the correct result. What do you think?
I haven't checked your arithmetic, but you seem to have the right idea.
 

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