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The Draining of a Fluid from a Pool by Gravity

The Draining of a Fluid from a Pool by Gravity. Submitted by: Jeffrey Fontenot Drew Ford MaryCynthia Ezike Rosalyn Pillow. Given. A swimming pool of unknown dimension W x Y x h This pool drains through a long pipe. Sketch. Assumptions. turbulent flow constant temp. constant velocity

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The Draining of a Fluid from a Pool by Gravity

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  1. The Draining of a Fluid from a Pool by Gravity Submitted by: Jeffrey Fontenot Drew Ford MaryCynthia Ezike Rosalyn Pillow

  2. Given • A swimming pool of unknown dimension • W x Y x h • This pool drains through a long pipe

  3. Sketch

  4. Assumptions • turbulent flow • constant temp. • constant velocity • constant viscosity • constant friction • constant dimensions of both pipe and pool • incompressible fluid • neglect minor losses • fully developed flow

  5. Find • Find a general equation that finds the time it takes to drain a swimming pool filled to height h with a fluid • Find the time to drain a pool of given dimensions filled with 1) water and 2) glycerin

  6. Calculations • First we relate the pool to the pipe • This relates the fall of the fluid in the pool to the speed at which it exits the pipe

  7. Calculations con’t Finding the head loss, this can be seen in eq. 6.39 of the book

  8. Calculations con’t After some algebra we find that the final equation is this. We can apply this equation to any dimensions or fluids

  9. Calculation cont. In the final equation is the very general version and we need to manipulate it so it will be able to show the difference between the two different fluids of water and Glycerin. The friction factor fav can be found by using the equation

  10. Calculation cont. This Reynolds number is found by using a equation containing the properties of a fluid that is its density and viscosity. This the Reynolds number is assumed to be that same for both fluids the equation to find V can be set up as a proportion.

  11. Calculations Cont. Finally plugging in the values of density and viscosity each of the fluids into the equation will give as a fluid velocity proportional to the other fluid. This finally gives the proportion of:

  12. Conclusion This proportion makes sense with the kinematic viscosity of Glycerin being much higher than that of the water. The glycerin ,at the same Reynolds number, will empty out of the pool much faster than the water.

  13. Biomed Application • This idea could be carried into biofluids in any intravenously applied fluid from a gravity drip. The fluids could range from simple saline to blood.

  14. Questions ?

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