Fundamentals of fluid loading Flashcards
What is the governing Laplace’s equation for 2D potential flow?
∂²ϕ/∂x² + ∂²ϕ/∂y² = 0
What boundary condition is applied at the cylinder surface?
The normal component of velocity at the surface is zero:
u_r = 0 on r = D/2
What is the velocity potential
ϕ for uniform flow past a cylinder?
ϕ = U₀ (r + D²⁄4r) cos(θ) for r > D⁄2
The velocity potential solution is easiest to obtain in ______ coordinates.
polar
What are the velocity components in polar coordinates?
u_r = ∂ϕ/∂r, u_θ = (1/r) ∂ϕ/∂θ
What is the Bernoulli equation used for fluid loading around a cylinder?
∂ϕ/∂t + (1/2)(u² + v²) + p/ρ + gz = constant
The Bernoulli equation assumes the fluid is ________ and ________.
inviscid, irrotational
What is the expression for fluid pressure from potential flow using Bernoulli?
p = −ρ ∂ϕ/∂t − (1/2) ρ (u² + v²)
Pressure varies with both __________ and __________ in unsteady flow.
time, position
True or False: The force on a body in a fluid comes only from dynamic pressure.
False – it also includes pressure due to unsteadiness.
True or False: Both unsteady potential and kinetic energy contribute to the force on the cylinder.
True
Boundary Layer?
Region within which viscoisty produces strong shear
In real fluids what is the pressure difference caused by?
Flow seperation
