9.10:
Fluid Pressure
Pressure is defined as the magnitude of force per unit area. Considering an incompressible fluid, the force can be expressed in terms of specific weight or fluid density.
Consider four points in water. The pressure is the same for all points at the same depth from the surface, but less at shallow depths. The pressure increases linearly with depth from the surface.
According to Pascal's law, the pressure intensity at any given point in an incompressible static fluid is the same in all directions.
Assume a wedge-shaped infinitesimal fluid element of unit width. The force on each side is expressed as the product of pressure and area.
As the liquid is at rest, the sum of the horizontal and vertical components of the forces should be zero.
Taking the horizontal components and using trigonometric relations, the equations are simplified to obtain px equal to ps.
Similarly, considering the vertical components, the equations are simplified to obtain py equal to ps.
So, the pressure at any point is the same in all directions.
9.10:
Fluid Pressure
In mechanical engineering, fluid pressure plays a critical role in designing systems that utilize liquid flow, such as hydraulic systems, pumps, and valves. When designing these systems, engineers must ensure they can withstand the forces created by fluid pressure to avoid damage or failure.
According to Pascal's law, a fluid at rest will generate equal pressure in all directions. This pressure is measured as a force per unit area, and its magnitude depends on the fluid's specific weight or mass density and the depth of the point of measurement from the surface of the fluid. We can express this relationship mathematically as p = ρgz, where ρ is the fluid density, g is the acceleration due to gravity, and z is the depth.
It should be noted that the equation, as mentioned above, is valid for incompressible fluids, such as most liquids, but not for gases, whose density changes considerably with both temperature and pressure. To understand how this equation applies to liquids, consider three points located inside water. At the same depth from the surface, the pressure is identical for all three points. However, the pressure is lower at shallow depths. The pressure increases linearly with depth as one moves farther from the surface.
Suggested Reading
- Hibbeler, R.C. (2016). Engineering Mechanics: Statics. Fourteenth Edition, New Jersey: Pearson. Pp. 512.