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Analyzing Hydrostatic Force on Vertical Walls in Compressible Fluids

This presentation explores the concept of hydrostatic force acting against vertical walls submerged in soft liquids, taking into account the compressibility of fluids. We derive an analytic expression for the hydrostatic force exerted on a wall of width 'b' and depth '-h'. The study compares analytical results with computational findings, demonstrating the similarity of hydrostatic forces for incompressible and compressible fluids. Applications in biomedical engineering highlight the role of hydrostatic forces in physiological processes and the implications for medical conditions such as apoplexy.

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Analyzing Hydrostatic Force on Vertical Walls in Compressible Fluids

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  1. BIEN 301Group Project PresentationHydrostatic Force Against A Wall Jasma Batham,Mootaz Eldib, Hsuan-Min Huang,Sami Shalhoub

  2. Problem • In the soft liquids, it may be necessary to account for liquid compressibility in hydrostatic calculation. The approximate density relation would be or . Use this approximation to show that the density variation with depth in a soft liquid is . Then consider a vertical wall of width b, extending from the surface (z=0) down to depth z=-h. find an analytic expression for the hydrostatic force F=(Þgh2b)/2 on this wall.

  3. Assumptions • Hydrostatic – water is not moving • Viscosity is not concerned • Steady static : sum of forces = 0 • For compressible fluid, density is variable • Multidimensional

  4. Simplifications • The horizontal component of the hydrostatic force is not required since the wall is not horizontal. So we are only concerned with the vertical component.

  5. Sketch

  6. Solution Equation 2.18 is: [1] From the problem it was given that: [2] Equating equation 1 and 2 gives: [3]

  7. Equation 2.17 says that: [4] Putting equation 4 in 3 we get: [5] Solving the differential equation to get [6]

  8. Now plugging equation 6 in: [7] We get: [8] equation 2.35 in the book tell us: [9]

  9. Computational Results

  10. Comparison of Analytical and Computational Results, with Discussion • To compare the analytical and computational, we got exactly same result. • Our results for incompressible hydrostatic force (equation 8) is equivalent to the solution that was provided by the instructor when p0 goes to zero. • Comparing the hydrostatic force for incompressible and compressible fluid we notice that they are very similar to each other. We can see that from the graph in the next slide

  11. Incompressible and compressible flow Vs. height of the Wall When both forces were graph against the height of the wall, they both came out to be pretty much equal, so incompressible force is a good approximation for the comprisable force

  12. BME Application • Apoplexy is one of the result in which blood vessel is broken by the hydrostatic force. • We can utilize the concept of hydrostatic force to determine what the force we should apply for clip blood pressure. • Our bodies will tell us when we should urinate because the hydrostatic force is acting on the urinary bladder.

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