What is the Derivation of delta(Pa)/delta(Pb) in Terms of Da and Db?

In summary, Bernoulli's Principle is a scientific law that states that as the speed of a fluid increases, its pressure decreases. This principle is the basis for the lift force in flight, where air flowing over a curved surface creates a difference in pressure that generates lift. The equation for Bernoulli's Principle is P + 1/2ρv^2 + ρgh = constant, and it has many real-life applications such as in airplane wings and medical devices. Two common misconceptions about Bernoulli's Principle are that the shape of an airplane's wing creates lift and that it can explain the lift of a spinning ball.
  • #1
Filththenwah
1
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Homework Statement



Using these equations:

1) Vb/Va = (Da/Db)^2
and
2) Va^2 = (2(Pa-Pb)) / [density*((Da/Db)^4)-1]

Derive a mathematical expression for delta(Pa)/delta(Pb) in terms of Da and Db

Homework Equations



1) Vb/Va = (Da/Db)^2
2) Va^2 = (2(Pa-Pb)) / [density*((Da/Db)^4)-1]

The Attempt at a Solution



No idea where to start.
Should I solve for Va^2 in equation 1 and sub that into equation 2 and solve for Pa and Pb?
 
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  • #2
That would give me two equations with two unknowns, so I could solve them. But then how do I get delta(Pa) and delta(Pb)?
 

Related to What is the Derivation of delta(Pa)/delta(Pb) in Terms of Da and Db?

What is Bernoulli's Principle?

Bernoulli's Principle is a scientific law that states that as the speed of a fluid increases, its pressure decreases. This relationship between speed and pressure is known as the Bernoulli effect.

How does Bernoulli's Principle apply to flight?

Bernoulli's Principle is the basis for the lift force that allows airplanes to fly. As air flows over the curved surface of an airplane's wing, the air on top moves faster than the air on the bottom, creating a difference in pressure that generates lift.

What is the equation for Bernoulli's Principle?

The equation for Bernoulli's Principle is P + 1/2ρv2 + ρgh = constant, where P is pressure, ρ is density, v is velocity, g is the acceleration due to gravity, and h is height.

What are some real-life applications of Bernoulli's Principle?

Bernoulli's Principle has many real-life applications, including airplane wings, sails on boats, and carburetors in cars. It is also used in medical devices such as ventilators and nebulizers.

What are some common misconceptions about Bernoulli's Principle?

One common misconception is that the shape of an airplane's wing is what creates lift. In reality, it is the difference in air pressure created by the air flow over the wing that generates lift. Another misconception is that Bernoulli's Principle can explain the lift of a spinning ball, when in fact the Magnus effect is responsible for this phenomenon.

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