# How can the pressure be more in liquid flowing with less speed?

• Frigus
In summary, Bernoulli's theorem states that the pressure in a fluid decreases as its velocity increases, in order to conserve energy. This can be practically explained by understanding that pressure relates to the microscopic kinetic energy of the fluid molecules. The equation ##\frac{1}{2}\rho v^2## represents the addition of microscopic and macroscopic kinetic energy, as well as potential energy, which is all conserved in the fluid. This explanation is more simplified and practical, compared to more complex conservation arguments. Additionally, this can be seen by multiplying the equation by volume and recognizing that pressure relates to energy. Therefore, pressure is conserved in order to maintain a balance of energy in the fluid.
Frigus
Before I have read Bernoulli's theorem I believed that pressure is more in liquid flowing with more speed but today I have read Bernoulli's theorem where this theorem says that the pressure is more in liquid flowing with lesser velocity please tell me how can this explained,with equation I understood that if if velocity is more so as to conserve energy pressure should be more but how can be this explained practically.

Hemant said:
I understood that if if velocity is more so as to conserve energy pressure should be more but how can be this explained practically
I am not sure what would count as a practical explanation if conservation of energy does not.

russ_watters
Dale said:
I am not sure what would count as a practical explanation if conservation of energy does not.
Sir but I can't understand how pressure can be energy.

Hemant said:
Sir but I can't understand how pressure can be energy.
Pressure isn't energy. Please post the units of pressure and the units of energy and compare them.

russ_watters said:
Pressure isn't energy. Please post the units of pressure and the units of energy and compare them.
Sir units of pressure are N/m^2 and units of energy are Nm,so why we are conserving pressure

well pressure has same units as Energy/volume that is same units as energy density...

Delta2 said:
well pressure has same units as Energy/volume that is same units as energy density...
Sir I want to know why we need to conserve pressure

Hemant said:
Sir I want to know why we need to conserve pressure
because pressure relates to the microscopic kinetic energy of the molecules of the fluid. Also it has same units as energy per unit volume

Delta2 said:
because pressure relates to the microscopic kinetic energy of the molecules of the fluid. Also it has same units as energy per unit volume
And why we write 1/2 rho v^2 if we are adding microscopic kinetic energy

The term ##\frac{1}{2}\rho v^2## is for the mAcroscopic kinetic energy. So we are adding microscopic kinetic energy(the pressure term) plus macroscopic kinetic energy (the##\frac{1}{2}\rho v^2## term) plus potential energy (the ##\rho gh## term) and this sum is conserved. That's Bernoulli's principle abit oversimplified perhaps.

Delta2 said:
The term ##\frac{1}{2}\rho v^2## is for the mAcroscopic kinetic energy. So we are adding microscopic kinetic energy(the pressure term) plus macroscopic kinetic energy (the##\frac{1}{2}\rho v^2## term) plus potential energy (the ##\rho gh## term) and this sum is conserved. That's Bernoulli's principle abit oversimplified perhaps.
Thanks sir

Delta2
Hemant said:
how can be this explained practically.
Here's a good arm waving explanation. If the fluid is flowing faster in one place than another, there must have been a force (differential) to accelerate it. That implies the higher pressure is in the region where the fluid came from . So its speed increases and its pressure decreases.
Of course there are conservation arguments which are more erudite and complete but the above is certainly very "practical".

jbriggs444, Dale and Delta2
Hemant, you are replying immediately to the messages you get, I think you will have a better outcome if you think about what people say before responding - it can take a few moments.

russ_watters, anorlunda and weirdoguy
sophiecentaur said:
Here's a good arm waving explanation. If the fluid is flowing faster in one place than another, there must have been a force (differential) to accelerate it. That implies the higher pressure is in the region where the fluid came from . So its speed increases and its pressure decreases.
Of course there are conservation arguments which are more erudite and complete but the above is certainly very "practical".
Thanks sir,it is what I was founding.

sophiecentaur
Vanadium 50 said:
Hemant, you are replying immediately to the messages you get, I think you will have a better outcome if you think about what people say before responding - it can take a few moments.
Thanks sir,physics forum is a place where I don't get answers to only questions but people like you help me to develop myself.

sophiecentaur and Dale
Hemant said:
Sir units of pressure are N/m^2 and units of energy are Nm,so why we are conserving pressure
Delta2 said:
well pressure has same units as Energy/volume that is same units as energy density...
This may be water under the bridge by now, but what I was after was a deconstruction of Bernoulli's equation (but I was on my way to bed...). It isn't readily apparent how pressure relates to energy, but it becomes obvious if you back out of the derivation.

If you multiply the standard form of Bernoulli's equation through by volume, then P becomes PV, which should be recognizable as energy, like when you push down on a piston-pump. 1/2ρV2 becomes 1/2mv2, which is kinetic energy. So that's how you see they are part of a conservation of energy statement, and dividing through by volume gives you the standard form, with the funny sounding units of "energy per unit volume".

Last edited:
Frigus, sophiecentaur and Dale
russ_watters said:
So that's how you see they are part of a conservation of energy statement, and dividing through by volume gives you the standard form, with the funny sounding units of "energy per unit volume".
Which is also why it only works for incompressible flow.

sophiecentaur
You have to admit my noddy explanation works every time.

Dale
Dale said:
Which is also why it only works for incompressible flow.
Sure, though it can be modified to work for compressible flow. Depending on the specifics of the flow and the assumptions, you can have varying density and temperature, and it starts to look a lot more like thermodynamics than fluids.

Dale
One missing detail in this is the assumption that there is no external forces involved in the fluids transition from slower speed to higher speed. The output from a fan is both higher pressure and higher speed because the fan performs work on the air. A classic example of Bernoulli is flow in a pipe. The source of energy to maintain the flow is ignored, and only the flow's interaction with the pipe is considered. Assuming no friction losses, and an incompressible fluid, then the energy per unit volume remains constant. If the kinetic energy increases due to an increase in velocity, such as a narrower section of the pipe, the the pressure energy decreases so that total energy remains constant.

Delta2 and russ_watters

## 1. How does the speed of liquid flow affect the pressure?

The speed of liquid flow directly affects the pressure. As the speed of flow increases, the pressure decreases. This is because faster-moving particles in the liquid collide with each other and the container walls less frequently, resulting in lower pressure.

## 2. Can the pressure be increased in liquid flow without changing the speed?

Yes, the pressure in liquid flow can be increased without changing the speed by increasing the density of the liquid. This can be achieved by increasing the temperature or by adding solutes to the liquid, such as salt in water.

## 3. How does the shape of the container affect the pressure in liquid flow?

The shape of the container can affect the pressure in liquid flow. A narrower container will result in higher pressure, as the same amount of liquid is forced into a smaller space, increasing the collisions between particles and the container walls.

## 4. What is the relationship between pressure and viscosity in liquid flow?

Viscosity, or the resistance of a liquid to flow, has an inverse relationship with pressure in liquid flow. As the viscosity of a liquid increases, the pressure decreases, as the particles in the liquid are more likely to collide with each other and the container walls, resulting in higher pressure.

## 5. How can the pressure be measured in liquid flow?

The pressure in liquid flow can be measured using a pressure gauge, such as a manometer or a pressure transducer. These devices measure the force exerted by the liquid on a given area, which is then converted into pressure units, such as pounds per square inch (psi) or pascals (Pa).

Replies
17
Views
2K
Replies
48
Views
4K
Replies
2
Views
6K
Replies
8
Views
1K
Replies
32
Views
4K
Replies
2
Views
2K
Replies
9
Views
2K
Replies
27
Views
3K
Replies
6
Views
2K
Replies
5
Views
1K