Tank Drainage Velocity: Does Area Matter?

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In summary, the conversation discusses the use of Bernoulli's equation to calculate the velocity of fluid draining from a tank and whether the area of the drainage hole should be considered. While the mass continuity principle suggests that the area should have an impact, Bernoulli's equation simplifies to only include height. The conversation also touches on the difference between velocity and volumetric flow rate, and how Bernoulli's equation relates velocity to pressure, similar to the relationship between pressure and force.
  • #1
UMath1
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Using Bernoulli's equation to calculate the velocity of fluid draining from a tank seems to give no weightage to the area of the drainage hole. But based on the mass continuity principle, the area of the hole should have an impact. Does the area of a drainage hole have an impact on the fluid velocity or not? And why does it appear to be neglected in velocity calculations?
 
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  • #2
The drainage opening does appear in the velocity, e.g. here. What calculation scheme are you referring to ?
 
  • #3
Yes that's a first. But still it does not appear in the equations used to calculate the velocity which is Bernoulli's equation. Bernoulli's equation simplifies to V =(2gh)^(1/2). This does not include the diameter of the hole.
 
  • #4
Velocity isn't volumetric flow rate. The volumetric flow rate depends on the velocity and area. Bernoulli's equation relates velocity to pressure.

It is similar to the difference between pressure and force. You don't necessarily need to relate them.
 

Related to Tank Drainage Velocity: Does Area Matter?

1. What is tank drainage velocity?

Tank drainage velocity is the rate at which a liquid drains out of a tank or container, usually measured in gallons per minute (GPM) or liters per minute (LPM).

2. How is tank drainage velocity calculated?

The formula for calculating tank drainage velocity is: V = (0.408 x Q) / A, where V is the drainage velocity in feet per second, Q is the flow rate in gallons per minute, and A is the cross-sectional area of the tank outlet in square feet.

3. Why does area matter in tank drainage velocity?

The area of the tank outlet directly affects the velocity of the draining liquid. A larger area means a larger opening for the liquid to flow out of, resulting in a higher drainage velocity. Conversely, a smaller area will result in a lower drainage velocity.

4. How does tank shape impact drainage velocity?

The shape of the tank can also affect the drainage velocity. For example, a tank with a conical bottom will have a lower drainage velocity compared to a tank with a flat bottom, as the conical shape creates more resistance to the flow of liquid.

5. What are some factors that can influence tank drainage velocity?

Aside from area and shape, other factors that can impact tank drainage velocity include the viscosity of the liquid, the height of the liquid in the tank, and the presence of any obstructions or blockages in the outlet. These factors should be taken into consideration when calculating and predicting the drainage velocity of a tank.

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