Homework Statement
The velocity components in a plane (i.e., 2-D) flow are measured at four points as indicated in the sketch at the bottom of this page (see attached doc. I wrote in the coords). The velocity components at the respective points are, in units of cm/sec:
u_a=5, v_a=2...
Oh,right. So it would be 8/sqrt(65)*i + 1/sqrt(65)*j
Then dot grad(T) with this, and eval @ (2,3) to get dT/dS = 1152/sqrt(65)*i + 177/sqrt(65)*j?
Is this correct?
x=(4y^2-30)/3*i
y=y*j
So, S=(4y^2-30)/3*i + y*j
dS=(8/3)y*i+1*j
eval @ (2,3),
dS=8*i+1*j
So, I do (8xy^2*i + (8x^2y+9y^2)*j) DOT (8*i + 1*j) to get dT/dS
Is this correct?
But if I parametrize the equation in terms of only y, there will be no x to plug in the 2 of the (2,3) point. I would have curve=(4y^2-30)/3 i + 1 j. Differentiating that would give me (8/3)y i evaluated at (2,3).
Sorry, I'm still a little confused. I see how you got x=(), but then are you saying I differentiate that equation, x(y), or do I plug that into T for x, and take grad(T)?
Homework Statement
A two-dimensional temperature field is given by the expression T=4x^2y^2+3y^3
(a) What is the magnitude and direction of the temperature gradient at the point (2,3)?
(b) What is the change in temperature dT/dS at the point (2,3) in a direction along the curve 3x-4y^2=-30...
Hi, I am a student pursuing an MS in Aerospace Engineering with a concentration in Aerospace Structures. I am currently taking a course in Stability of Structures. The "required" textbook is Guide to Stability Design Criteria for Metal Structures (ISBN 0471127426), and the other recommended text...
Homework Statement
Prove that the magnitude of the impact parameter B equals the length (-b) of the hyperbolic semiminor axis.
Homework Equations
|B|=|b|=|a|sqrt(e^2-1)
The Attempt at a Solution
I really don't know where to start. I was thinking of finding a relation between a...