Calculate stagnation pressure, static pressure, fluid density, fluid speed, or Mach number for Bernoulli and isentropic flow conditions.

Bernoulli assumes steady, incompressible, lossless flow at one elevation; pressures must share a reference. Isentropic gas calculations require absolute pressure and constant ฮณ; shocks and losses are excluded.

Preset densities are illustrative; use density at your fluidโ€™s actual temperature and pressure.

Stagnation Pressure Formula

The following Bernoulli formula applies to steady, incompressible, lossless flow at the same elevation, using one pressure reference. For a calorically perfect gas brought to rest isentropically, use absolute pressures and Pโ‚€/P = [1 + (ฮณโˆ’1)Mยฒ/2]^(ฮณ/(ฮณโˆ’1)); shocks and losses are excluded.

Pstag = Pstatic + 1 / 2 ร— p ร— vยฒ
  • Where Pstag is the Stagnation Pressure (Pa)
  • Pstatic is the static pressure (Pa) 
  • p is the fluid density (kg/m^3) 
  • v is the fluid speed (m/s) 

To calculate the stagnation pressure, multiply the density by the velocity squared, divide by 2, then add the static pressure to the result.

How to Calculate Stagnation Pressure?

The following example problems outline how to calculate the Stagnation Pressure.

Example Problem #1

  1. First, determine the static pressure (Pa). In this example, the static pressure (Pa) is given as 10.
  2. Next, determine the fluid density (kg/m^3). For this problem, the fluid density (kg/m^3) is given as  1250.
  3. Next, determine the fluid speed (m/s). In this case, the fluid speed (m/s) is found to be 5.
  4. Finally, calculate the Stagnation Pressure using the formula above: 

Pstag = Pstatic + 1/2 * p * v^2

Inserting the values from above and solving yields: 

Pstag = 10 + 1/2 * 1250 * 5^2 = 15635 (Pa)

FAQ

What is the significance of calculating Stagnation Pressure in fluid dynamics?

Stagnation pressure is crucial in fluid dynamics as it represents the total pressure a fluid attains when it is brought to a stop isentropically from a given velocity. This measure is essential for understanding the energy characteristics of a fluid flow, including its potential to perform work when decelerated. It is widely used in the design and analysis of wind tunnels, jet engines, and various aerodynamic components to ensure optimal performance and safety.

How does fluid density affect the Stagnation Pressure?

Fluid density directly influences the stagnation pressure. According to the stagnation pressure formula (P_stag = P_static + ยฝฯvยฒ), an increase in fluid density (ฯ) leads to a higher dynamic pressure component (ยฝฯvยฒ), thereby increasing the total stagnation pressure. This constant-density relation is appropriate only when compressibility is negligible. Compressible gas flow requires the isentropic relation or another model suited to its losses and shocks.

Can Stagnation Pressure be less than the static pressure?

No, stagnation pressure cannot be less than the static pressure. For the incompressible Bernoulli model, stagnation pressure is static pressure plus dynamic pressure (which is nonnegative). The dynamic pressure represents the kinetic energy per unit volume of the fluid flow, which adds to the static pressure when the fluid is brought to a stop isentropically. Therefore, the stagnation pressure is always equal to or greater than the static pressure.