Bernoulli's Equation is one of the most important/useful equations in fluid mechanics. Many problems relating to real fluid are analyzed with a form of the Bernoulli equation.  

This calculator has Bernoulli's Equation Solved for:

• Bernoulli's Pressure
• Bernoulli's Velocity
• Bernoulli's Elevation

Based on the continuity equation and conservation of energy where total energy, Potential Energy and Kinetic Energy, are conserved, Bernoulli stated that:

    `P + 1/2 rho * V^2 + rho *g*h = C`    where: C is a constant.

In a combined system of non-compressible fluids, Bernoulli asserted that the relationship of pressure, density, velocity and elevation can be equated in Bernoulli' Equation: 

   `P_1 + ½ rho * V_1^2 + rho *g*h_1 =  P_2 + ½ rho * V_2^2 + rho *g*h_2`

Bernoulli's Equation solved for Pressure is:

          `P_1 = ρ*g [(V_2^2 -V_1^2)/(2*g) + (h_2-h_1)  + P_2/(ρ*g)]`

Bernoulli's Equation solved for Velocity is:

         `V_1 = sqrt(V_2^2 +2 *g* (h_2-h_1)  + 2/rho(P_2 -P_1) )`

Bernoulli's Equation solved for Elevation is:

         `h1 = (P_2 - P_1 + ρ*g*h2+1/2*ρ*v2^2-1/2*ρ*v1^2)/(ρ*g)`

where:

• V₁ is the velocity at elevation 1
• P₁ is the pressure at elevation 1
• h₁ is the height of elevation 1
• P₂ is the pressure at elevation 2
• V₂ is the velocity at elevation 2
• h₂ is the height of elevation 2
• ρ is the density of the fluid
• g is the acceleration due to gravity

References

• Young, Hugh and Freeman, Roger.  University Physics With Modern Physics.  Addison-Wesley, 2008. 12th Edition, (ISBN-13: 978-0321500625 ISBN-10: 0321500628 ) Pg 468, eq 14.17
• Instructional Video by Paul Andersen on Youtube