Thursday

October 2, 2014

October 2, 2014

Posted by **Ash** on Friday, October 11, 2013 at 6:03am.

u = y,

v = −x

The streamlines are circles centered at the origin, and this flow is an example of a solid-body rotation.

As shown in the figure, a small square fluid element is placed at the point (x,y)=(0,1) at t=0: it moves and distorts with the fluid. Assume that the flow is incompressible.

All of your answers below should use only x, y, Δt, ρ. In the answer boxes, use Dt to denote Δt and rho for ρ.

1) In the first part of this problem, we only consider the fluid element. Determine the angles Δθx and Δθy of the fluid element at some small later time t=Δt.

2) Compute the flow's vorticity field.

ωx=

ωy=

ωz=

3) Compute the rate of strain.

εxx=

εyy=

εxy=

4) Compute the substantial derivatives Du/Dt and Dv/Dt

Du/Dt=

Dv/Dt=

5) For this particular flow, fτi=0. Using the x- and y-momentum equations, find expressions for the components of the pressure gradient ∇p.

∂p∂x=

∂p∂y=

6) Integrate the pressure gradient components to find an expression for p(x,y)−p(0,0).

Is the flow rotational or irrotational?

**Answer this Question**

**Related Questions**

Fluid Mechanics - Consider the 2D, incompressible, steady flow between parallel ...

Physics - In a machine, an ideal fluid with a density of 0.9*10^3 kg/m^3 and a ...

Fluid Mechanics - Water at 600F flows steadily through a horizontal circular ...

FLUID MECHANICS - For oil (SG =0.86 and μ = 0.025 Ns/m2) flow of 0.5 m3/s ...

classical mechanics - enturi Flow Meter (19 points possible) A Venturi flow ...

Chemistry/Physics - The equation needed to solve for volumetric flow rate = flow...

classical mechanics - A Venturi flow meter is used to measure the the flow ...

Physics Classical Mechanics - A Venturi flow meter is used to measure the the ...

Fluid Mechanics - . A plate of mass M is suspended between two opposing jets, ...

physics - The flow rate of a liquid through a 2.0cm radius pipe is 0.0080 m^3/s...