8.1.4. Approximation of Pressure using Taylor Series

Try these first

1. 1.

   What happens to shear stress in a fluid at rest?

   Hint

   Think about the forces acting on stationary fluid.

2. 2.

   Define gauge pressure.

   Hint

   Consider the pressure difference from atmospheric levels.

3. 3.

   What is the primary reason shear stress is zero in a resting fluid?

   • It acts parallel to the surface
   • It is a function of velocity
   • Fluid is not in motion

   Hint

   Think about the conditions required for shear to occur.

4. 4.

   True or False: Gauge pressure is always positive.

   • True
   • False

   Hint

   Consider what happens at low pressure levels.

5. 5.

   A fluid at rest has a gauge pressure of 30 kPa at a depth of 2 m. Calculate the absolute pressure considering atmospheric pressure is 101.3 kPa.

   Hint

   Remember to sum both pressures to find the absolute pressure.

6. 6.

   Using the Taylor series, approximate the pressure at a point P(3, 2, 1) knowing P(2, 2, 1) = 100 kPa and the pressure gradient in the x direction is 5 kPa/m.

   Hint

   Consider how Taylor series expansions function when calculating nearby point values.