Pressure variation in a rotating tube

However, in this case, we can assume that the tube is long enough for the pressure to be only dependent on r (axial symmetry). Therefore, the pressure distribution can be described as P(r) = P0 + rho*w^2*r^2/2, where P0 is the pressure at the axis (r=0). Using this equation, we can calculate the pressure at r=2m to be P(2m) = P0 + rho*w^2*2^2/2 = P0 + 4*rho*w^2. In summary, the pressure distribution as a function of r is given by P(r) = P0 + rho*w^2*r^2/2 and the pressure at
  • #1
boileroo
12
0

Homework Statement


An enclosed vertical tube rotates about its vertical axis at w=3000rpm. At the axis, r=0, P=1.5bar and T=293K.

What is the pressure distribution as a function of r? And hence calculate the pressure at r=2m.

The Attempt at a Solution



I have seen this type of questions before with a horizontal tube, where the pressure difference across an element is balanced out by the centripetal force (ie [P-(P+dP)]A = rho*A*w2*r dr).

I would appreciate some help adapting this to work for the tube aligned vertically as stated above. Obviously the mass of the element must also be taken into account, but I am struggling to figure out how! Thank you
 
Physics news on Phys.org
  • #2
Consider a volume dV at position [tex](r, \phi, z)[/tex]. Then:
_ The pressure on the 2 vertical sides<---> Centripetal force (that is, considering P(r,z) and P(r+dr,z))
_ The pressure on the 2 horizontal sides <---> Weight (that is, considering P(r,z) and P(r,z+dz))
In general, pressure is a function of not only r but also z: P = P(r,z).
 

1. What is the cause of pressure variation in a rotating tube?

The main cause of pressure variation in a rotating tube is the centrifugal force. As the tube rotates, the centrifugal force acts on the fluid inside, causing it to move away from the axis of rotation. This results in a decrease in pressure near the axis and an increase in pressure near the outer wall of the tube.

2. How does the rotation speed affect pressure variation in a rotating tube?

The rotation speed of the tube directly affects the magnitude of pressure variation. As the speed increases, so does the centrifugal force, resulting in a greater pressure difference between the center and the outer wall of the tube.

3. Does the diameter of the tube have an impact on pressure variation?

Yes, the diameter of the tube also affects pressure variation. A larger diameter tube will have a smaller pressure difference compared to a smaller diameter tube. This is because the centrifugal force is spread out over a larger area in a larger diameter tube, resulting in a smaller pressure gradient.

4. How does fluid viscosity play a role in pressure variation in a rotating tube?

Fluid viscosity, or its resistance to flow, can impact pressure variation in a rotating tube. Highly viscous fluids will experience larger pressure differences compared to low viscosity fluids, as the centrifugal force is more effective in moving the fluid away from the axis of rotation.

5. Are there any practical applications of studying pressure variation in rotating tubes?

Yes, there are several practical applications of studying pressure variation in rotating tubes. One example is in centrifugal separators, where the pressure difference is used to separate different components of a fluid. This concept is also utilized in centrifugal pumps and turbines to generate pressure and energy.

Similar threads

Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
20
Views
956
Replies
1
Views
504
  • Introductory Physics Homework Help
Replies
6
Views
2K
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
14
Views
957
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Linear and Abstract Algebra
Replies
16
Views
1K
Back
Top