Flow Rate of Water vs. Orifice Diameter: Get Help

[ConceptuallyInept]

One would assume that when the area of an orifice is doubled then twice as much water will flow through this orifice. Hence we assume a proportional relationship between the two. However use of a garden hose leads us to believe that increasing the area of the orifice decreases the velocity of the water hence implying an inverse relationship.

I need a theoretical relationship between the diameter of a circular orifice and the flow rate of water discharged from this orifice.

Your help would be greatly appreciated

 

[HallsofIvy]

I don't see the "however". If, indeed, twice as much water flowed through twice the area, that would imply that the velocity of the water stays the same! What are you assuming is constant? The pressure on the water?

 

[wais]

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The relationship between the diameter of an orifice and the flow rate of water discharged from it is complex and depends on various factors such as pressure, viscosity of the fluid, and surface tension. However, in general, there is a direct relationship between the two.

According to Bernoulli's principle, as the diameter of an orifice increases, the velocity of the fluid passing through it decreases. This is because the same amount of fluid must pass through a larger area, resulting in a decrease in velocity. This is what we observe in a garden hose, where increasing the diameter of the nozzle leads to a decrease in the velocity of the water.

However, this decrease in velocity is accompanied by an increase in the cross-sectional area of the flow, resulting in a larger volume of water being discharged. This is why we still see an increase in flow rate even though the velocity decreases.

Theoretical equations, such as the Bernoulli's equation and the continuity equation, can be used to calculate the exact relationship between orifice diameter and flow rate. However, it is important to note that these equations are based on ideal conditions and may not always accurately represent real-world scenarios.

In practical applications, factors such as turbulence, friction, and irregularities in the orifice can affect the flow rate and may not follow the theoretical relationship. Therefore, it is important to consider these factors and conduct experiments to determine the specific relationship between orifice diameter and flow rate for a particular system.

In conclusion, while there is a general direct relationship between orifice diameter and flow rate, it is important to consider other factors that may affect the flow rate in a real-world scenario. I hope this helps and I am happy to assist with any further questions or clarifications.