Consider the continuity, and momentum (Euler) equations in the absence of body forces: др ² + · (pv) = ( V. 0 Ət VP P DV Dt (a) Expand the continuity and all three components of Euler's equation in cylindrical coordinates making no simplifications. др a Ət Ər (b) Axisymmetric flow is a specific case of flow in cylindrical coordinates in which there is no velocity component in the circumferential direction (ua = 0) and for which circumferential symmetry exists (0/00 = 0). Demonstrate that for axisymmetric flow, the continuity and momentum equations (in the absence of body forces) simplify to: -(pur) + = 0 + Ur Ә — (puz) + ! 0 pur T əz dur 10P + 0 dur du, +21= 82 Ət ər por du₂ duz du₂ 10P +U₂ Ət Ər əz рдz + U₂' + 0
Consider the continuity, and momentum (Euler) equations in the absence of body forces: др ² + · (pv) = ( V. 0 Ət VP P DV Dt (a) Expand the continuity and all three components of Euler's equation in cylindrical coordinates making no simplifications. др a Ət Ər (b) Axisymmetric flow is a specific case of flow in cylindrical coordinates in which there is no velocity component in the circumferential direction (ua = 0) and for which circumferential symmetry exists (0/00 = 0). Demonstrate that for axisymmetric flow, the continuity and momentum equations (in the absence of body forces) simplify to: -(pur) + = 0 + Ur Ә — (puz) + ! 0 pur T əz dur 10P + 0 dur du, +21= 82 Ət ər por du₂ duz du₂ 10P +U₂ Ət Ər əz рдz + U₂' + 0
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![3. Consider the continuity, and momentum (Euler) equations in the absence of body forces:
+ ()=0
DV VP
+
Dt
P
Ət
(a) Expand the continuity and all three components of Euler's equation in cylindrical
coordinates making no simplifications.
(b) Axisymmetric flow is a specific case of flow in cylindrical coordinates in which there
is no velocity component in the circumferential direction (up = 0) and for which
circumferential symmetry exists (0/00 =0). Demonstrate that for axisymmetric flow,
the continuity and momentum equations (in the absence of body forces) simplify to:
Ә
+ (pu₂) +
Ət Ər
dur
Ət
du₂
Ət
dur
Ər
duz
+ Uhr gr
+ U₂
Ә
Əz
= = 0
pur
T
dur 10P
+
əz
·(pu-) +
+2=²
+ U₂'
por
duz 10P
+
дz paz
0
= 0
-
= 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ed04b1a-8ef1-487d-ab34-a2261f9ce8a1%2F026998f2-c097-47b4-b37c-1717f2956c88%2Fwqqxm7c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Consider the continuity, and momentum (Euler) equations in the absence of body forces:
+ ()=0
DV VP
+
Dt
P
Ət
(a) Expand the continuity and all three components of Euler's equation in cylindrical
coordinates making no simplifications.
(b) Axisymmetric flow is a specific case of flow in cylindrical coordinates in which there
is no velocity component in the circumferential direction (up = 0) and for which
circumferential symmetry exists (0/00 =0). Demonstrate that for axisymmetric flow,
the continuity and momentum equations (in the absence of body forces) simplify to:
Ә
+ (pu₂) +
Ət Ər
dur
Ət
du₂
Ət
dur
Ər
duz
+ Uhr gr
+ U₂
Ә
Əz
= = 0
pur
T
dur 10P
+
əz
·(pu-) +
+2=²
+ U₂'
por
duz 10P
+
дz paz
0
= 0
-
= 0
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