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Thread starter
jontyjashan
Start date
Jun 30,Tags
In summary: I don't understand how pressure and area would have anything to do with velocity.The pressure provides the energy that is converted into kinetic energy which can be expressed in Bernoulli's equation. The area has no impact on the velocity. pressure=energy\times velocity
jontyjashan
Science Advisor
This question is worded quite poorly if you ask me. When people say that a liquid is flowing with a lot of pressure, they often mean that it exerts a lot of force upon a stationary object; or more plainly, it has a high velocity.
If we are to look at pressure alone, then there are two pressures to consider: the pressure just before the fluid leaves the container, and the pressure afterwards. The pressure just before it leaves the container is simply the hydrostatic pressure that you have listed [tex]p = \rho g h[/tex]. As the fluid then leaves the container, this pressure or energy is converted into kinetic energy, which can be illustrated in Bernoulli's equation which basically says that along a steamline the pressure energy + the velocity energy + the height equals a constant. Now, the final pressure is simply the pressure of the air, ambient.
So, whatever case has the higher initial pressure has the higher velocity. However, this is not pressure, as both fluids will leave at atmospheric pressure.
Science Advisor
Homework Helper
jontyjashan said:
Hi jontyjashan!Well, pretend there's onlyhole, and that the density of water is 1 'what speed will the water leave the hole?
jontyjashan
First of all there is only 1 container and 1 fluid not 2 fluids.minger said:
First of all there is only 1 container and 1 fluid not 2 fluids.how can water from both holes leave with the same pressure.It is simple logic.What wordings inthe question you did not understand by the way.I just want to know from which hole water will come out with more velocity
Science Advisor
I understood the wordings [sic] better than you explained them. Pressure != velocity. Remember that. Any jet discharging into the atmosphere will have an internal pressure of 0 gauge. However, I was trying to explain to you the difference between the two.
Now, onto velocities. Before anyone simply throws you the answer, why don't you give it a try. What do you know, what do you need to find? What are you looking for?
jontyjashan
sorry ,If i said something wrong but
if we do this experiment practically,velocity of water from the upper hole is much high
but if we look at it mathematically,velocity of water from the lower hole should be high
RoyalCat
jontyjashan said:
Yes, you are incorrect. Take the limit of the 'upper hole', the very top of the container of liquid. The velocity at which it exits the container is 0, it does not leak out at all!Interestingly enough, the maximumdistance the water will reach isn't achieved from a hole at either extreme, but from a hole at the very middle. :)
Science Advisor
Homework Helper
jontyjashan said:
Hi jontyjashan! Thanks for the PM.Yes, mathematically the speed depends only on the pressure, and therefore on the depth, not on the size of the hole.Did you do the experiment yourself?How did you measure the water coming out of the two holes?
RoyalCat
tiny-tim said:
Yes, mathematically the speed depends only on the pressure, and therefore on the depth, not on the size of the hole.
Did you do the experiment yourself?
How did you measure the water coming out of the two holes?Hi jontyjashan! Thanks for the PM.Yes, mathematically the speed depends only on the pressure, and therefore on the depth, not on the size of the hole.Did you do the experiment yourself?How did you measure the water coming out of the two holes?
Wouldn't the fact that [tex]P\propto{Area^{-1}}[/tex] have a say in that?So that means that the acceleration the pressure provides to the liquid is inversely proportional to the area of the hole it's bursting through, doesn't it? (Sorry for the poor wording, by the way. Haven't dealt with pressure properly yet)And the acceleration it provides to the liquid, is what determines its exit velocity, and this would be determined by making an equation something like the following, right?[tex]a=\frac{P}{mA}[/tex][tex]a=Acceleration, A=Area, P=Pressure[/tex][tex]P=\rho gh[/tex][tex]a(A,h)=\frac{\rho gh}{mA}[/tex]So the acceleration, and in turn, exit velocity, is directly proportional to the height, and inversely to the area, isn't it?Sorry if I'm way off on this, this is just my intuition talking here, other than knowing the units of pressure, I'm lost, haha!
Science Advisor
The velocity is inversely proportional compared to the area in the case of pipe flow or when the fluid is forced through the opening. In this case of a free jet, where the inlet can be assume to be an infinite resevoir, this is not the case.
The fact of any disparities you may see in a small experiment would be in any difficulties keeping the level of the fluid high enough such that constant pressure is maintained in both holes.
Science Advisor
Homework Helper
RoyalCat said:
Sorry, RoyalCat, but you're just burbling.
RoyalCat
tiny-tim said:
Sorry, RoyalCat, but you're just burbling.
:shy:Guess I should give this a try once I actually study hydrodynamics, heh.
jontyjashan
i have tried this experiment practically,and i found that from the upper hole water just trickles out but from the second all the water comes out very fast
Science Advisor
Homework Helper
jontyjashan said:
But thatmathematically correct!(I'd thought you were saying it was the other way roundAt the lower hole, there is more pressure , so the watercome out faster.
Science Advisor
Just so we don't confuse him tiny...
At the lower hole, just before the hole there is more pressure, which is a function of depth. That pressure then becomes atmospheric as the fluid leaves the hole, with the energy being converted into kinetic energy, the difference in pressure being the driving force.
modulus
As minger mentioned, the experiment is practically impossible, because it is not possible to keep a uniform pressure while the water flows out of the holes.
But, if we take this theoretically and conceptually, the hole from which water comes out with more pressure (considering an infinite reservoir of water), is the one from which water goes a larger horizontal distance.
So, I think we might try to attempt this by figuring out the initial velocity with which the water comes out from each hole, and then, use that knowledge to figure out the horizontal range (considering each water particle is a projectile under horizontal projection) with the formula u*sqrt(2h/g).
But, here, we come at another problem- if we use this formula, we must consider the area around the infinite reservoir to be a vaccum, and, if we consider that, then, the water inside the reservoir would have infinite pressure (being exerted on the walls of the container).
Or, we can use the formulas of projectile motion which also consider drag provided by air... but I don't know those...
jontyjashan
For more information, please visit hydraulic expansion of heat exchanger tubes.
ya,there is need to find the range of the water from both holes.but is it necessary that water having more range will have more velocity
Homework Helper
jontyjashan said:
You need to find the range? I thought you just needed to find out which hole water will rush out faster from.Also, no, it's not true that higher velocity = higher range. If the hole is too close to the ground, then the water will get to travel almost no distance at all before hitting the ground. if the hole is too high, the water's exit velocity would be very low. Somewhere between those two extremes is the height that gives the longest range.
jontyjashan
thats a part of it
jontyjashan
ideasrule said:
i think what you said is not true
modulus
ideasrule said:
Jontyjashan, he's not wrong, he's completely correct.And, mabey the initial velocity with which the liquid comes out does not determine its pressure.Again, I agree with minger, the question is worder wrongly- as soon as the water comes out of the vessel, its pressure becomes equal to that of the external environment, so, mabey you want to ask that 'from which hole will come out with greater force'.
jontyjashan
first of all i have already clarified that i wanted to ask by which hole will the water come out with more velocity and secondly can you give me a proof to show Higher Velocity is not equal to higher range.come out with things of your own.Just don't keep on agreeing with everyone
modulus
Well, if you want to find out the hole from which water comes out with a higher velocity, here you go:
Firstly, we know that the water exerts an equal pressure on all sides of the vessel, so we can use the pressure exerted by the liquid, in the horizontal direction at the respective point, and then figure out the force with which the water comes out. Next, figure out the relation betwen force and velocity and you'll get your answer for each hole.
At least, I agree with everyone, instead of contradicting their every statement when they are trying their level best to help you. You better remember that we are just 9th graders and they've got a lot more knowledge than us. So, I'd advise you to stop using your arrogant and hostile attitude towards everyone, and just try to learn a bit of something from them.
Think twice about what you're going to say before you say it.
modulus
The water accelerates out of the vessel with an instantaneous acceleration (I think). Now we'll just have wait for the dudes who know about differential equations to get online before we can proceed.
jontyjashan
I am not here for contradicting everyone.I just try to derive sense from every word they speak and i don't blindly agree with them.This site is for help and not for arguement.Sorry if I said something wrong but my attitude is like this.
Secondly i also know my limits . Dont try to show a domineering,dominating and patronising attitude.
Again what you said in this post, I don't agree with it .Can you give detailed explanation
modulus
The force with which the liquid comes out mass*v-0/time.
Here, the initial velocity is zero, and the time is negligible, making the acceleration instantaneous. Since the acceleration of the particles of water are zero, we'll hae to use differential equations- I don't know how to use them.
Let's not fight, and focus on the question.
Please.
I'm sorry if I said anything that hurt you.
jontyjashan
lets both of us put our brains together.
First of all initial velocity is not zero.
Secondly are we considering only one jet of water or are we taking the water to be infinite
modulus
Can't we talk about this later? I'm getting tired
Homework Helper
When you say the height of the hole is 1.5 m am 0.5 m, I presume that they are from the bottom of the container to the center of the hole. The velocity of the water molecules on the horizontal diameter of the hole will be the same and is equal to sqrt(2gh). The velocities of the molecules above the diameter will gradually decrease and below the diameter the velocities will gradually increase. But the average velocity will be approximately the velocity of the molecules at the center of the hole. So the velocity of the out flow does not depend on the diameter of the hole. It only depends on the depth of the hole from the water surface. The rate of outflow depends on the diameter of the hole.jontyjashan said:
Homework Statement
There is a container of height 2 m
it is filled with water upto the brim
there are 2 holes made in it
one hole of area 5cm^2 is made at a height of 1.5 m
another hole of area 10cm^2 is made at a height of 0.5m
through which hole will the water rush out with more pressure
When you say the height of the hole is 1.5 m am 0.5 m, I presume that they are from the bottom of the container to the center of the hole. The velocity of the water molecules on the horizontal diameter of the hole will be the same and is equal to sqrt(2gh). The velocities of the molecules above the diameter will gradually decrease and below the diameter the velocities will gradually increase. But the average velocity will be approximately the velocity of the molecules at the center of the hole.It only depends on the depth of the hole from the water surface. The rate of outflow depends on the diameter of the hole.
queenofbabes
Do you understand Bernoulli's equation? If you use that the problem is pretty trivial...
Pressure in liquids is the force per unit area that a liquid exerts on its container. It is caused by the weight of the liquid above and is measured in units of force per unit area, such as Pascals or pounds per square inch.
Pressure in liquids is caused by the weight of the liquid above, while pressure in gases is caused by the collisions of gas molecules with the walls of the container. Additionally, pressure in liquids is not affected by changes in volume, unlike pressure in gases.
The factors that affect pressure in liquids include the density of the liquid, the depth of the liquid, and the acceleration due to gravity. The pressure also increases with depth due to the weight of the liquid above.
Pressure in liquids can be measured using a device called a manometer, which measures the height of a liquid column in a tube. It can also be measured using pressure gauges or by using the equation P = ρgh, where P is pressure, ρ is density, g is acceleration due to gravity, and h is the depth of the liquid.
Pascal's law states that when pressure is applied to a confined liquid, the pressure is transmitted equally in all directions. This means that an increase in pressure at one point in a liquid will result in an equal increase in pressure at all other points in the liquid. This law is used to explain how hydraulic systems, such as car brakes, work.
Fluid is typically defined as any substance that cannot maintain a shearing or tangential force when it is at rest. It goes through continuous variation in shape when exposed to such stress. The major characteristic of fluids is the constant position change of one section of the material relative to different parts under shear stress. On the other hand, consider shearing forces in elastic solids that are held in a flexed or twisted orientation; such solids do not undergo flow and can easily revert back to their original shape. Compressed fluids can come to their stable shape, but the forces between the container and fluid or forces within the fluid should not be shear forces. The fluids apply an outward pressure known as hydrostatic pressure that is predominantly perpendicular to the container's surface.
Fluid Pressure
Fluid pressure is the measure of the force exerted by the fluid per unit area on a body in the fluid or on the closed container's surface. This pressure can be generated by any acceleration or by outside forces on the closed container. Such fluids have no distinct shape, and their pressure is exerted in every direction. This pressure can be enhanced through variations in the fluid's velocity and hydraulic processes. In the case of water in a lake, pressure at the lake's bottom is approximately equivalent to the weight of the water column divided by the column's area. When a person stands on a pool's bottom (without floating), there will be a water column of about the diameter of the person's head all the way up to the bottom, pushing the whole body down. The value of fluid pressure on the head can be calculated by dividing the weight of the water column by the weight of the area of the head. Normally, to counter the external pressure, the human body raises the internal body pressure according to the external forces engulfing the body. As the depth increases, the water pressure can be very high, and after some point, the human body will not be able to withstand the pressure.
In the case of atmospheric pressure, dividing the weight of the air column by the area of the top of the person's head gives the air pressure on the top of the head. When a weather report shows high pressure, this implies that the air column reaches up higher than it reaches for lower air pressure readers. A barometer calculates the weight of the air column or the air pressure. This type of pressure is created by the weight of all the air many miles above the affected body. Even though this pressure is very high, human bodies generate enough internal pressure that balances out the air pressure. The average air pressure in Delhi is less than in Leh. This is due to the higher altitude of Leh, which implies that its air column is not as tall as in Delhi. This also implies that a pressurised snack pack (made in Delhi) will expand when it is brought to Leh. As it is brought to a lower pressure area, it may even explode as per the extent of the condition.
Fluid Pressure Effects
The main quantities that impact fluid pressure are heating, motion, and chemical changes. The motion of fluids such as rivers, wind and sea waves can exert pressure on objects proportional to the surface area perpendicular to the motion's direction. A streamlined shape decreases the effective pressure on the submerged objects. When fluids are heated, it generally expands. If fluids are heated inside an enclosed vessel, the expansion will attract more internal pressure. Heating balloons will cause them to expand. Chemical reactions that release gases will raise the pressure inside a vessel. In many cases, chemical reactions will speed up if there is a variation in fluid pressure. Shaking a carbonated beverage will increase the production of gases and the fluid pressure inside the bottle.
Daniel Bernoulli found out that the air pressure in a pipe decreases when the air velocity in the pipe increases. This is called Bernoulli's Principle. One of the best applications of this concept is employed in aeroplanes and other flying crafts. The wings of aeroplanes are typically flat on the bottom and curved on the top. When air travels over the curved top section of the wing, the speed increases due to the speciality of the shape. This directly reduces the pressure relative to the bottom section of the wing. The less pressure on the top part produces the lift needed to maintain the aeroplane in ideal motion.
This video explains the application of Bernoulli's principle
1) What is meant by pressure?
Pressure is the force exerted perpendicular to the surface of a body per unit area along which that force is applied.
2) What are the main types of pressures?
Absolute pressure, gauge pressure, differential pressure and sealed pressure are the main types of pressure.
3) What is meant by gauge pressure?
Gauge pressure is defined as the pressure relative to the ambient pressure.
4) What is fluid?
A fluid is a gas, liquid or other substance that constantly deforms under an applied external force. An ideal fluid has practically zero shear modulus. In simpler terms, they are materials which cannot withstand any type of shear force exerted on them.
5) What are the main types of fluids?
The main types of fluids are steady or unsteady, compressible or incompressible and viscous or non-viscous.
6) What is meant by fluid pressure?
Fluid pressure is the measure of the force exerted by the fluid per unit area on a body in the fluid or on the closed container's surface. This pressure can be generated by any acceleration or by outside forces from the closed container. Such fluids have no distinct shape; their pressure is exerted in every direction. This pressure can be enhanced through variations in the fluid's velocity and hydraulic processes.
7) What are the impacts of fluid pressure?
The impacts of fluid pressure are heating, motion, and chemical changes. The motion of fluids such as rivers, wind and sea waves can exert pressure on objects proportional to the surface area perpendicular to the motion's direction. A streamlined shape decreases the effective pressure on the submerged objects. When fluids are heated, it generally expands. If fluids are heated inside an enclosed vessel, the expansion will attract more internal pressure. Heating balloons will cause them to expand.
8) Give an example of variation of fluid pressure between two places with different altitudes.
The average air pressure in Delhi is less than in Leh. This is due to the higher altitude of Leh, which implies that its air column is not as tall as in Delhi. This also implies that a pressurised snack pack (made in Delhi) will expand when it is brought to Leh. As it is brought to a lower pressure area, it may even explode as per the extent of the condition.
9) The fluids apply an outward pressure known as _____ pressure that is predominantly perpendicular to the container's surface.
Answer: hydrostatic
Explanation: The fluids apply an outward pressure known as hydrostatic pressure that is predominantly perpendicular to the container's surface.
10) Explain the direction of fluid pressure.
The pressure generated by fluids not only pushes down at a particular point, but also pushes up and to the sides. On every side, pressure is the same. This is due to the nature of gases and liquids to adapt to the container's shape. This also implies that any hollow vessel immersed in a liquid has pressure on the entire surface, bottom and top. When a person swims underwater, the water pressure increases as the depth increases. The fundamental reason that we do not feel the pressure is the counterpressure produced by our bodies to nullify this crushing force. The body acts like a fully blown balloon under such pressure. As the body goes deeper, the water pressure will increase and will overcome the body's internal pressure. This will result in fatal health and physical issues.
11) What are the main quantities that impact fluid pressure?
The main quantities that impact fluid pressure are heating, motion, and chemical changes. The motion of fluids such as rivers, wind and sea waves can exert pressure on objects proportional to the surface area perpendicular to the motion's direction. If fluids are heated inside an enclosed vessel, the expansion will attract more internal pressure. Chemical reactions that release gases will raise the pressure inside the vessel. In many cases, chemical reactions will speed up if there is a variation in fluid pressure.
12) _____ found out that the air pressure in a pipe decreases when the air velocity in the pipe increases.
Answer: Daniel Bernoulli
Explanation: Daniel Bernoulli found out that the air pressure in a pipe decreases when the air velocity in the pipe increases.
13) What is the most familiar application of Bernoulli's principle?
One of the best applications of Bernoulli's principle is employed in aeroplanes and other flying crafts. The wings of aeroplanes are typically flat on the bottom and curved on the top. When air travels over the curved top section of the wing, the speed increases due to the speciality of the shape. This directly reduces the pressure relative to the bottom section of the wing. The less pressure on the top part produces the lift needed to maintain the aeroplane in ideal motion.
1) What is Bernoulli's principle?
2) What is meant by hydrostatic pressure?
3) What is hydraulics?
4) What is the average atmospheric pressure?
5) What is viscosity?
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