How Much Water Flows Through a 6mm Hole in a Tank Per Second?

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Homework Help Overview

The problem involves fluid dynamics, specifically the flow of water through a small circular hole in a tank. The hole has a diameter of 6 mm and is located 14 m below the water level, with the top of the tank open to the air. The original poster seeks to determine the volume of water discharged per unit time after calculating the speed of efflux.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the speed of efflux and the volume flow rate. There are suggestions to consider the area of the hole and the concept of flux to calculate the volume discharged per unit time. Some participants question the original poster's approach and encourage thinking in terms of unit analysis.

Discussion Status

The discussion is ongoing, with participants providing hints and guidance on how to approach the calculation of volume flow rate. There is no explicit consensus, but several lines of reasoning are being explored regarding the relationship between speed, area, and volume.

Contextual Notes

Participants note the importance of unit analysis and the relationship between speed and area in determining the volume flow rate. The original poster has already calculated the speed of efflux, which is a key component in the subsequent calculations.

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A small circular hole 6.00 mm in diameter is cut in the side of a large water tank, 14.0 m below the water level in the tank. The top of the tank is open to the air.

i found the first speed
What is the speed of efflux?
16.6 m/sCorrect



now it asks me to find the volume discharged per unit time

What is the volume discharged per unit time?
 
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anyone, help??
 
badman said:
anyone, help??

you're so close by thinking in terms of flux!

the rate of change in volume is given by the flux of the velocity of the fluid through that area.

so think how to calculate that... (unit analysis will work!) :-p
 
If you have the speed through the hole and the area of the hole, you should be able to figure out the volume flow rate. Think of a tube of fluid leaving the hole. In a given time, how long would the tube be? And what would its volume be?
 
nvm...
 
...Av
 

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