Extend the results found in Example 1.5, and determine the forms of f, . u, V 2

Question:

Extend the results found in Example 1.5, and determine the forms of ∇f, ∇. u, V2f, and ∇ ×u for a three-dimensional cylindrical coordinate system (see Fig. 1.5).

Fig 1.5

0 X3 N e3 2 z eo X

Example 1.5

Consider the two-dimensional case of a polar coordinate system as shown in Fig. 1.8. The differential length

Fig 1.8

X2 (0) 8 r X1

Equation 1.94

(ds) = (hde)  + (hd5) + (h3d5)

Equation 1.95

1= e2 @3: dxk ds dx ek = -ek = ds2 dxk ek ds3 1 ax* h,  Tek 1 ax ezek h a 1 xk h30kThe basic vector differential operations then follow to be 1  r 30 V= - + @o  1  Vo = er -teo- ar r 30 1 a rr

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question
Question Posted: