Skip to content

Bernoulli’s Equation 1: Pitot Tube Velocity

December 17, 2011

I have created a new and better article: Pitot Tube and Pressure Explanation With F1 and Pikes Peak Example.

One of the most well known aerodynamic equations is Bernoulli’s Equation:

\frac{P_1}{\rho} + \frac{1}{2} V_1^{2} = \frac{P_2}{\rho} + \frac{1}{2} V_2^{2}

The equation can be used with the following simplifying assumptions:

  • Inviscid, frictionless flow
  • Imcompressible flow
  • Steady State
  • Works for flow along a Streamline

Before getting into the derivation of the equation lets look at a common example.

Example

A common use of the Bernoulli Equation is calculating the stream velocity through measured pressure.

Assume all the required conditions exist, let’s see what the velocity is if the Static Pressure is 101KPa and the Total Pressure is 105KPa.

\frac{P_1}{\rho} + \frac{1}{2} V_1^{2} = \frac{P_2}{\rho} + \frac{1}{2} V_2^{2}

\frac{101000}{1.225} + \frac{1}{2} V_1^{2} = \frac{105000}{1.225} + \frac{1}{2} 0^{2}

V_1 = 80.8[\frac{m}{s}]

Equivalent to this is the form I typically use which gets the same answer (this comes from my preferance of not having denominators):

P_1 + \frac{1}{2} \rho V_1^{2} = P_2 + \frac{1}{2} \rho V_2^{2}

or, in notation similar to the photo from NASA:

P_s + \frac{1}{2} \rho V^{2} = P_t

Bernoulli’s Equation has many uses, so whenever the 4 assumptions I listed are reasonable it is a very quick way to find an unknown velocity, static pressure, or total pressure.

Another article will be written to better explain this. It will be found somewhere on The Aerodynamics Page of ConsultKeithYoung. You can also find more related articles by using the sitemap on that site and choosing Pitot Tube.

References:

 This is my main Fluid Mechanics book in college and I think it’s a very good one.

http://en.wikipedia.org/wiki/Bernoulli’s_principle

Advertisements
Leave a Comment

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: