Why Does Differential Pressure Vary As The Square Of The Flow?

In summary, differential pressure in fluid dynamics varies as the square of the flow due to the relationship between flow rate and pressure drop in a system. According to Bernoulli's principle and the continuity equation, as the flow velocity increases, the kinetic energy of the fluid rises, leading to a corresponding increase in pressure drop across an obstruction or within a conduit. This relationship demonstrates that changes in flow rate have a quadratic effect on pressure differentials, illustrating the inherent physics governing fluid behavior in various systems.
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chevywaldo
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TL;DR Summary
Can someone explain to me Bernoulli's principle as to why the pressure across a restriction varies as the square of the velocity? I'm looking for an understanding (conceptual) as to why this is without a gazillion math examples please. Thanks.
Can someone explain to me Bernoulli's principle as to why the pressure across a restriction varies as the square of the velocity?

I'm looking for an understanding (conceptual) as to why this is without a gazillion math examples please. Thanks.
 
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chevywaldo said:
Can someone explain to me Bernoulli's principle as to why the pressure across a restriction varies as the square of the velocity? I'm looking for an understanding (conceptual) as to why this is without a gazillion math examples please. Thanks.
Bernoulli's principle is simply conservation of energy, of a small mass of fluid.

Kinetic energy is proportional to velocity squared.
Potential energy is proportional to pressure difference.

In physics, follow the energy, as it changes form.
 
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  • #3
That doesn't answer the question.

Yes I can explain it using math myself, but that's not the point.

Sometimes in physics it's necessary (and often more useful) to understand "why" something happens instead of using only math to show explain. If you only use math to understand physics then you really don't have a full understanding of the principles of why something is or isn't.
 
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And sometimes there isn't. What sort of answer are you looking for?
 
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chevywaldo said:
That doesn't answer the question.

Yes I can explain it using math myself, but that's not the point.

Sometimes in physics it's necessary (and often more useful) to understand "why" something happens instead of using only math to show explain. If you only use math to understand physics then you really don't have a full understanding of the principles of why something is or isn't.
He... didn't use math. I am very confused by your response.
 
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chevywaldo said:
it's necessary (and often more useful) to understand "why" something happens

​
 
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boneh3ad said:
He... didn't use math. I am very confused by your response.
Having seen earlier posts by chevywaldo, I knew that he liked to argue, and needed to be seen to be proved right. So I was very careful to answer this question, using only the mathematical words that he had used in his OP.

It has been a week since he cast his baited hook into PF, and I carefully pinched his bait. He had warned us that he had a gazillion mathematical barbs on his hook. I believe he has now gone off in frustration, to some other fishing hole under a bridge, where he can play at being a more successful troll.
 
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Thread closed temporarily for Moderation...
 
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A very insulting post by the OP has been deleted, and OP is on a 10-day vacation from PF. This thread will remain closed. Thanks everybody for trying to help the OP with their question.
 
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FAQ: Why Does Differential Pressure Vary As The Square Of The Flow?

What is differential pressure in fluid dynamics?

Differential pressure refers to the difference in pressure between two points in a fluid system. It is a crucial parameter in understanding how fluids flow through pipes, ducts, or other conduits, as it drives the movement of fluid from areas of higher pressure to areas of lower pressure.

Why does flow rate influence differential pressure?

The flow rate of a fluid is directly related to the differential pressure across a flow restriction, such as an orifice or a valve. As the flow rate increases, the fluid experiences more resistance due to friction and turbulence, resulting in a higher differential pressure required to maintain that flow rate.

How is the relationship between flow rate and differential pressure mathematically expressed?

The relationship is often expressed using the Bernoulli equation or the Darcy-Weisbach equation, where the differential pressure (ΔP) is proportional to the square of the flow rate (Q). This means that if the flow rate doubles, the differential pressure increases by a factor of four, illustrating the square relationship.

What factors can affect the differential pressure in a system?

Several factors can influence differential pressure, including the viscosity of the fluid, the diameter and length of the pipe, the roughness of the pipe's interior surface, and the presence of any fittings or obstructions. Changes in these parameters can alter the flow characteristics and, consequently, the differential pressure.

How can engineers use the concept of differential pressure in design?

Engineers can use the concept of differential pressure to design systems that optimize fluid flow, ensuring that pumps, valves, and piping are appropriately sized to handle expected flow rates. By understanding how differential pressure varies with flow, they can create more efficient systems that minimize energy consumption and reduce wear on equipment.

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