Question

This is my third attempt. The first two attempts were completely wrong, because the people who answered never used the Navier Stokes Equaqtions. I need to know what parts of the equations will go to zero and why. So if the answer does not start out by writing the N-S Equations and crossing out terms that will be zero, the answer is not being answered correctly. Please actually read the question. I am looking for the answer using CYLINDRICAL COORDINATES. Please don't copy and paste the answer because this is not the same question.

Starting with the Navier-Stokes and continuity equations in CYLINDRICAL COORDINATES, estimate the volumetric flow rate of honey flowing downward through a long vertical soda straw due to gravity. Do a reality check to make sure your answer makes sense.

Answer 1

Solution:- The solution for this probpem can be obtained By Using Navier stokes and continuity equations as follows -

Assumption to apply Navier stoke equation-

a) Assume a coordinate system and determine the direction of flow.

b) To determine the mote information, continuity equation should be apllied alon with Navier stoke's equation.

c) Elimintae the terms that are zero.

d) Direction of g should be in correct direction.

e) Integrate the resulting equation and boundary condition should apply properly.

Calculation :- The flow through soda straw of honey can be obtained as follows-

Applying Boundary condition we can get-

If pressure is same at both side due to atmospheric pressure. the pressure gradient will be zero. put rha value of P_L - P_o = 0,and we get-

also if R= neglegible

Where - ve sign denotes the downward direction of flow.