How Do You Calculate the Pressure Gradient in a Tube with Flowing Orange Juice?

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SUMMARY

The discussion focuses on calculating the pressure gradient in a tube with flowing dilute orange juice, specifically using the equation Vmax = (Change in P * R^2)/(4*viscosity*L). The assumptions for solving the problem include laminar flow with a Reynolds number of 2100, treating the orange juice as a Newtonian fluid, and assuming its density is equivalent to that of water. Participants emphasize the necessity of calculating the specific Reynolds number for the flow and suggest using the Darcy-Weisbach correlation for accurate results.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically laminar flow.
  • Familiarity with the Reynolds number calculation.
  • Knowledge of Newtonian fluids and their properties.
  • Basic understanding of pressure gradient equations in fluid mechanics.
NEXT STEPS
  • Calculate the specific Reynolds number for the given flow conditions.
  • Research the Darcy-Weisbach correlation for pressure loss in pipes.
  • Explore viscosity calculations for non-Newtonian fluids.
  • Study the implications of varying flow rates on pressure gradients in tubes.
USEFUL FOR

Engineering students, fluid mechanics practitioners, and anyone involved in the analysis of fluid flow in pipes will benefit from this discussion.

corinnab
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a very dilute orange juice flows along a smooth tube (0.010m in diameter) with a maximum flow rate of 0.1m/s.
a) State the assumptions needed to solve the problem
b) Calculate the pressure gradient

Equations:
Vmax = (Change in P * R^2)/(4*viscosity*L)

Reynolds number = (density*D*v)/viscosity

I am a bit confused about how to solve this as I havn't done any engineering before. This is what I have come up with so far:

a) Assume laminar flow - Reynolds number = 2100
Assume Newtonian fluid
Assume density of dilute orange juice is same as for water.

b) Use Reynolds number to solve for viscosity. Then solve for change in pressure/L using Vmax equation.

Any help would be appreciated!
 
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The Reynolds number is not always 2100 for laminar flow. You need to calculate the Re for this particular flow. Google Darcy-Weisbach correlation
 
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