math
posted by paul gokool .
The radius of a sphere immersed in an infinite ocean of incompressible fluid with density
according to the equation, R(t) = A + a cos(nt), where R(t) is a function of time, t, and A,
constants, with ‘a’ being positive. The fluid moves radially under no external forces and
pressure at infinity is P¥. If the velocity potential, F , for the motion of the fluid is given
where f (t) is a function of time, then address the following:
(a) What is a reasonable assumption for the form of the velocity field, q , of the fluid?
(b) Show that the velocity, v , of the boundary is, v = −an sinnt r.
(c) By considering the boundary condition, find f (t).
(d) Determine the pressure at any point on the sphere using Bernouilli’s equation for unsteady
(e) Show that the maximum pressure attained on the sphere is,
= ¥ + +
A
3a
p P n a
2
r 2 .
Respond to this Question
Similar Questions

Physics
In a machine, an ideal fluid with a density of 0.9*10^3 kg/m^3 and a pressure of 1.3*10^5 Pa flows at a velocity of 6.0 m/s through a level tube with a readius of 0.5 cm. This tube connects to a level tube that has a radius of 1.5 … 
Physics
If I double the density of a fluid, the buoyant force on a given piece of material fully immersed in the fluid will? 
PHYSICS URGENT DUE IN 15 MINUTES
The figure below (a) shows a sphere with a radius of r = 157 mm (density ñ = 1.24 g/cm³) suspended in water by a string. The ball is completely submerged in the water and the string is attached from the bottom of the water tank to … 
Calculus
4. At time t, t>0, the volume of a sphere is increasing at a rate proportional to the reciprocal of its radius. At t = 0, the radius of the sphere is 1 and at t = 15 the radius is 2. a. Find the radius of the sphere as a function … 
physics
an ideal fluid in a pipe of diameter 14cm is moving at 6.0m/s. If the incompressible fluid density is 1.05grams/cc, what is the flow rate in kg/s and what is the speed of flow if the pipe narrows to 4.0cm radius? 
physics
The definition of an incompressible fluid is Select one: a. A fluid with a constant density at all pressures b. A fluid with no viscosity c. A fluid with a constant pressure d. A fluid with viscosity 
Physics and Maths
A sphere of uniform density d1 has a radius R. It also consists of a hollow sphere of radius r. the sphere floats slightly on water of density d2. Find r. 
Physics ( using earth to find pressure of planet y
3. A model of Earth’s interior: Look up the radius and mass of the Earth. Radius is 6,371 km Mass is 5.974 x 10^24 kg Calculate its average density. p_e = (5.974 x 10^24 kg)/ (4/3)pi r^3 = (5.974 x 10^24 kg)/ (4/3)pi (6371)^3 = 5.54 … 
Physics Using hydrostatic equilbrium)
3. A model of Earth’s interior: Look up the radius and mass of the Earth. Radius is 6,371 km Mass is 5.974 x 10^24 kg Calculate its average density. p_e = (5.974 x 10^24 kg)/ (4/3)pi r^3 = (5.974 x 10^24 kg)/ (4/3)pi (6371)^3 = 5.54 … 
Mechanical Engineering
The equation for flow in a circular pipe for a special kind of fluid, called a "powerlaw" fluid is given by v=(delP/2mL)^1/n * (n/n+1)*[R^(n+1/n)  r^(n+1/n)] where m and n are constants of the fluid, and delP/L is the change in pressure …