e) divp= (rp,) + t); f) curl p has components: ape de, ap: 1[a apr (rpe) - ae az az ar g) v²u is given by (3.66). au a a2U v²U = ar ar əz?
e) divp= (rp,) + t); f) curl p has components: ape de, ap: 1[a apr (rpe) - ae az az ar g) v²u is given by (3.66). au a a2U v²U = ar ar əz?
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Answer part e,f and g of the Question in the image uploaded.
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![Verify the following relations for cylindrical coordinates u = r, v = 0, w = z:
a) the surfaces r = const, 0 = const, z = const form a triply orthogonal family, and
a(x, y, z)
=r;
a(r, 0, z)
b) the element of are length is given by
ds? = dr² +r²d0² + dz?;
c) the components of a vector p are given by
P, = Px cos 0 + py sin 0,
Po = -Px sin 0 + Py cos 0, P: = P2i
d) grad U has components: aU làu aU.
e) divp= (rp,) + +r];
f) curl p has components:
ape
apr
apr
az
az
ar
ae
g) v²u is given by (3.66).
au
a?U
v²U =
ar
+
ar
a02
az?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1c4d217-886f-4958-b018-18e9293fbd17%2Ff2028f45-ea87-412a-8e79-9d3a497e7fed%2F60k65de_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Verify the following relations for cylindrical coordinates u = r, v = 0, w = z:
a) the surfaces r = const, 0 = const, z = const form a triply orthogonal family, and
a(x, y, z)
=r;
a(r, 0, z)
b) the element of are length is given by
ds? = dr² +r²d0² + dz?;
c) the components of a vector p are given by
P, = Px cos 0 + py sin 0,
Po = -Px sin 0 + Py cos 0, P: = P2i
d) grad U has components: aU làu aU.
e) divp= (rp,) + +r];
f) curl p has components:
ape
apr
apr
az
az
ar
ae
g) v²u is given by (3.66).
au
a?U
v²U =
ar
+
ar
a02
az?
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