Help: Volume Fluxes and Associated Velocities

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Discussion Overview

The discussion revolves around calculating average velocity and volume transport of ocean currents, focusing on the relationship between these variables in the context of physical oceanography. Participants explore mathematical formulations and clarify concepts related to volume transport and velocity.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant presents a scenario involving volume transport and asks for the average velocity of an ocean current based on given dimensions.
  • Another participant critiques the initial post for not adhering to the homework template and emphasizes the need for effort in formulating questions.
  • A participant expresses difficulty in understanding how to relate velocity, volume transport, and area, seeking clarification on these concepts.
  • One participant suggests focusing solely on volume rather than mass and provides the equation Q = vA for volumetric flow rate.
  • A later reply rearranges the equation to solve for velocity and performs a calculation, expressing uncertainty about the correctness of the answer in the context of a graduate-level course.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the initial question, as there are varying levels of understanding and differing approaches to the problem. Some participants focus on the mathematical formulation, while others emphasize the need for proper question structure.

Contextual Notes

There are limitations in the initial understanding of the concepts involved, and the discussion reflects a mix of mathematical reasoning and conceptual clarification without resolving the uncertainties expressed by participants.

Who May Find This Useful

This discussion may be useful for students in physical oceanography or related fields who are grappling with the concepts of volume transport and velocity in fluid dynamics.

geojon
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Suppose that volume transport of an ocean current is 50 x 10^6 m^3/s. Assume that this volume transport is carried in a current of uniform speed which is 50 km wide and 1 km thick. What is the average velocity of the current?

Suppose that the velocity of a current is 0.2 m/s. Assume that the width and thickness of the current are 50 km and 0.5 km respectively. What is the volume transport associated with this current, in m^3/s?
 
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The issue is that I am having a difficult time getting started. I know that velocity is the derivative of speed (or a position with relation to time). I also know that volume transport refers to a mass of water (or water parcel) moving through an area per unit time. What I cannot resolve, is how to relate these variables in order to come up with a formula. The question comes from my graduate level physical oceanography course; I am a transplant to the department (geologist by training). Any help at all would be greatly appreciated? Is my grasp on these terms correct?
 
Follow the homework layout and post in the correct forum.

Forget about mass, your question is only about volume.

This is the only equation you need:

Q = vA
(volumetric flow rate = velocity * area)
 
Thank you for your help. I will try moving forward with this equation.
 
Rearranging the equation Q = v*A to solve for velocity yields the following equation: v = Q/A

Plugging in the numbers we get: v = (50 x 10^6 m^3 s^-1) / (50,000,000 m^2) ...I have converted km to meters at this point

The answer then, is 1 meter/second.

I am not sure of this answer, as this is a graduate level course. The math is not wrong, though; is my approach?
 

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