Fundamentals of fluid loading

Question 1

What is the governing Laplace’s equation for 2D potential flow?

Answer 1

∂²ϕ/∂x² + ∂²ϕ/∂y² = 0

Question 2

What boundary condition is applied at the cylinder surface?

Answer 2

The normal component of velocity at the surface is zero:
u_r = 0 on r = D/2

Question 3

What is the velocity potential
ϕ for uniform flow past a cylinder?

Answer 3

ϕ = U₀ (r + D²⁄4r) cos(θ) for r > D⁄2

Question 4

The velocity potential solution is easiest to obtain in ______ coordinates.

Answer 4

polar

Question 5

What are the velocity components in polar coordinates?

Answer 5

u_r = ∂ϕ/∂r, u_θ = (1/r) ∂ϕ/∂θ

Question 6

What is the Bernoulli equation used for fluid loading around a cylinder?

Answer 6

∂ϕ/∂t + (1/2)(u² + v²) + p/ρ + gz = constant

Question 7

The Bernoulli equation assumes the fluid is ________ and ________.

Answer 7

inviscid, irrotational

Question 8

What is the expression for fluid pressure from potential flow using Bernoulli?

Answer 8

p = −ρ ∂ϕ/∂t − (1/2) ρ (u² + v²)

Question 9

Pressure varies with both __________ and __________ in unsteady flow.

Answer 9

time, position

Question 10

True or False: The force on a body in a fluid comes only from dynamic pressure.

Answer 10

False – it also includes pressure due to unsteadiness.

Question 11

True or False: Both unsteady potential and kinetic energy contribute to the force on the cylinder.

Answer 11

True