Energy and Momentum Equations

Question 1

Assumptions for Bernoulli’s equation

Answer 1

i) u is steady flow,
ii) the body forces F are conservative
iii) there is a one-to-one function relating pressure and density p = p(ρ) and ρ = ρ(p), or ρ is fixed and uniform.

Question 2

What is a barotropic fluid?

Answer 2

A fluid whose density is a function of pressure only.

Question 3

What is the vorticity vector?

Answer 3

ω = ∇ × u

Question 4

What is Bernoulli’s equation for steady flow? What does each term represent?

Answer 4

1/2 u.u + Ω + integral dp /ρ = constant along a streamline
kinetic energy per unit mass + potential energy of the external forces per unit mass + potential energy of the internal forces per unit mass.

Question 5

What is the flow speed in a Pitot-Static tube?

Answer 5

|U|^2 = 2ghρl/ρ

Question 6

Euler’s Momentum Theorem (Archimedes’ Principle)

Answer 6

R = - g triple integral (V) ρ dV = - Mg