How do you calculate total pressure in a pipe?

Total pressure in a pipe is calculated as the sum of static pressure and dynamic pressure.

Here's a breakdown:

• Total Pressure (P_total): The sum of the static and dynamic pressures, representing the total energy per unit volume of the fluid.

• Static Pressure (P_static): The pressure exerted by the fluid when it is not in motion. It's the pressure you would measure if you were moving along with the fluid.

• Dynamic Pressure (P_dynamic): The pressure associated with the motion of the fluid. It's proportional to the fluid's density and the square of its velocity.

The Formula

The relationship is expressed by the following equation:

P_total = P_static + P_dynamic

Where:

• P_total is the total pressure.
• P_static is the static pressure.
• P_dynamic = (1/2) ρ v²
  • ρ (rho) is the density of the fluid.
  • v is the velocity of the fluid.

Measuring Total Pressure

In practical applications, devices like a Pitot tube are used to measure total pressure. A Pitot tube measures the total pressure directly, while another port (or separate instrument) is used to measure the static pressure. By measuring both, you can calculate the dynamic pressure and, therefore, the velocity of the fluid.

Example

Let's say you have water flowing in a pipe.

• The static pressure (P_static) is measured to be 100,000 Pascals (Pa).
• The density of water (ρ) is approximately 1000 kg/m³.
• The velocity of the water (v) is measured to be 2 m/s.

Then, the dynamic pressure (P_dynamic) would be:

P_dynamic = (1/2) 1000 kg/m³ (2 m/s)² = 2000 Pa

Therefore, the total pressure (P_total) would be:

P_total = 100,000 Pa + 2000 Pa = 102,000 Pa

Key Takeaways

• Total pressure accounts for both the pressure of the fluid at rest and the pressure due to its motion.
• Pitot tubes are commonly used to measure total pressure in fluid flow scenarios.