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  • Doubt regarding Bernoulli theorem...

    Ankush Sharma

    Member

    Updated: Oct 25, 2024
    Views: 1.0K
    I have a doubt or you can say that I found a problem with Bernoulli theorem! So friends please tell me the solution for this - the doubt is that according to Bernoulli, whenever a fluid flows through pipe and during its path when there is decrease in diameter or area then the velocity of the fluid will increase so pressure will decrease(because velocity is inversely proportional to pressure as proved by Mr. Bernoulli).

    But according to the definition of pressure that is pressure is the ratio of force per unit area, means pressure is inversely proportional to area, so it means whenever there is any decrease in area then pressure increases (opposite to Bernoulli). So friends please tell me that why we are using Bernoulli's concept not pressure definition?

    Is there any fault in using pressure definition in this case? And if yes, then why?

    Edited By Admin: Tried to make the text more readable by editing SMS text.
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  • ISHAN TOPRE

    Member • Dec 21, 2012

    The definition of pressure measurement is correct. You are confusing between pressure measurement and pressure energy. Bernoulli's theorem gives relation between KE, PE, Datum energy etc. It works on law of conservation of energy (as per I law).

    Now, imagine a hollow tube in which fluid is flowing. from left to right. When you block the path of fluid, the pressure on the right of block is less as compared to the left portion. The case is same even of there is no sudden blockage and uniform or non uniform change of CSA.

    [​IMG]
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  • Ankush Sharma

    Member • Dec 21, 2012

    Issue
    The definition of pressure measurement is correct. You are confusing between pressure measurement and pressure energy. Bernoulli's theorem gives relation between KE, PE, Datum energy etc. It works on law of conservation of energy (as per I law).
    ok dear nice description, But are u sure that it is pressure energy which decreases due to decrease in area????? because i never read or listen about this ........... or u can say that i never give stress on energy written after pressure............... so dear please tell me that are u sure about ur reply????? Waiting.......
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  • areeba ronald nad

    Member • Dec 21, 2012

    I clearly disagree cause when there's a certain decrease in the area of the tube in which fluid is flowing then the pressure will definitely rise/increase leading to a definite increase in velocity..
    remember AV=k
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  • Ramani Aswath

    Member • Dec 21, 2012

    Anku2993
    ok dear nice description, But are u sure that it is pressure energy which decreases due to decrease in area????? Waiting.......
    Never get confused about basics.Pressure is always force/unit area. Bernoulli's theorem deal with fluid flow in a closed system. As #-Link-Snipped-# says it has to do with the first law of thermodynamics, which deals with conservation of energy.
    In a closed system where there is a fluid flow the sum of all the energies is constant. These energies are: 1. Potential - height of the point under consideration above a datum line, 2. Kinetic - due to the velocity of the fluid at that point and 3. Pressure at that point.

    For simplicity let us consider a horizontal pipe. Let us say that one end has an area less than the area at the other end. The quantity of water flowing is same at all points since there can be no accumulation or depletion in a closed system. This means that the velocity at the smaller end has to be higher than at the larger end proportional to the ratio of areas. This means that the kinetic energy is more at that point. Since the pipe is horizontal, the potential energy is the same. To conserve the total energy the pressure at the smaller end has to decrease. That is all there is to it. Your problem arises in equating the definition of pressure with the value of a particular pressure. You are comparing two different things.
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  • vikas reddy

    Member • Dec 21, 2012

    you are absolutely right sir
    it's actually a pure energy conversion
    as we all know that energy is neither created nor destroyed just changes its form
    simply the pressure energy is converted to kinetic energy
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  • Ankush Sharma

    Member • Dec 21, 2012

    bioramani
    Never get confused about basics.Pressure is always force/unit area. Bernoulli's theorem deal with fluid flow in a closed system. As #-Link-Snipped-# says it has to do with the first law of thermodynamics, which deals with conservation of energy.
    In a closed system where there is a fluid flow the sum of all the energies is constant. These energies are: 1. Potential - height of the point under consideration above a datum line, 2. Kinetic - due to the velocity of the fluid at that point and 3. Pressure at that point.
    .
    hi, very nice way of explaining it using flow rate............. i really appreciate it............ But according to ur first paragrph are u want to say that the pressure in closed system is entirely different from pressure defition????????? if yes then will u please explain me that what is pressure????? pressure is force per unit area, right...... but which area............ the area in which we are applying pressure,right............ now i am totally confused😳 ......... so will u please explain these things in details.............. waiting for ur valuable reply...........
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  • Ankush Sharma

    Member • Dec 21, 2012

    vikas reddy
    you are absolutely right sir
    it's actually a pure energy conversion
    as we all know that energy is neither created nor destroyed just changes its form
    simply the pressure energy is converted to kinetic energy
    it means it is the pressure energy which is decreasing due to decrease in area not pressure, right????
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  • Ramani Aswath

    Member • Dec 21, 2012

    Anku2993
    it means it is the pressure energy which is decreasing due to decrease in area not pressure, right????
    No, the pressure also decreases leading to decrease in pressure energy. The pressure has to decrease because the kinetic energy has increased.
    If the outlet is closed and no flow takes place, the pressure along a horizontal line will be the same. What you are seeing is because there is a flow.
    I feel that your confusion arises out of considering static pressure and the dynamic pressure together.
    Pressure is always force per unit area.
    The point is that when there is a flow the force varies at various points.
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  • rahul69

    Member • Dec 21, 2012

    According to my knowledge, as we know P = ρgh , in this case as vertical height of pipe decreases, hence pressure decreases 😁 . However, if I am wrong do correct me #-Link-Snipped-# sir .
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  • Ankush Sharma

    Member • Dec 21, 2012

    bioramani
    No, the pressure also decreases leading to decrease in pressure energy. The pressure has to decrease because the kinetic energy has increased.
    sir, i am not able to understand the things u explain....... so please simple tell me that is it the pressure or pressure energy which is decreasing?????????? waiting.... and how can u relate these things with static and dynamic pressure????
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  • Ramani Aswath

    Member • Dec 24, 2012

    Think of it this way.
    In a horizontal pipe potential energy will be same and can be ignored for discussion.
    If the diameter decreases, the velocity has to increase because the same quantity of fluid has to flow. Some force is needed to increase the velocity. A lower pressure is created at the smaller diameter. This leads to a positive pressure difference between the larger and smaller diameters. This differential force drives the velocity higher. The reverse happens when the flow is from a smaller to a larger diameter. In this case velocity decreases. To achieve this a negative pressure difference is needed. So the pressure increases down stream.
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  • Ankush Sharma

    Member • Dec 25, 2012

    bioramani
    Think of it this way.
    In a horizontal pipe potential energy will be same and can be ignored for discussion.
    If the diameter decreases, the velocity has to increase because the same quantity of fluid has to flow. Some force is needed to increase the velocity. A lower pressure is created at the smaller diameter..
    dear you are saying this thing because u already know this that velocity will increase with decrease in area, that's why u are saying that there must be positive pressure difference in order to satisfy the increase in velocity. But how can you say this thing that there must be positive pressure difference at that point, if you don't know that velocity will increase??? Because according to pressure definition pressure will increase with decrease in area, so according to this there will be flow moving from low pressure to high pressure, which is not possible. so dear how can u answer this??? waiting..
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  • Ramani Aswath

    Member • Dec 25, 2012

    What do you think makes water flow in a horizontal pipe. If you measure the inlet and out let pressure, you will find that the outlet pressure is less than the inlet. It is this differential that causes flow. If there is no differential water does not flow. In this case the pressure decreases because of pipe friction. This is included in the extended Bernoulli's equation.
    according to pressure definition pressure will increase with decrease in area
    That is true only if the force remains smae. The whole issue is that the force is not the same.
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  • vikas reddy

    Member • Dec 25, 2012

    pressu
    Anku2993
    it means it is the pressure energy which is decreasing due to decrease in area not pressure, right????
    pressure energy is a function of pressure.......
    primarily just move out of the basic definition of pressure i.e force per area
    think wisely that the condition "pressure is inversely proportional to area is valid only at constant force, but force is not a constant in moving liquid so you cannot apply your assumption in this case."
    we know that "Energy is neither created nor destroyed, it just changes it's form"
    apply this to Bernoulli's theorem.
    at outlet KE is increasing now from the law if KE is increasing then there should be a decrease in another form..
    the forces acting on the system are
    pressure, weight , kinetic energy
    can the mass of the system change???? nooooo, so weight is constant.
    what else can change now in order to satisfy the universal law conversation of energy ??????
    think of your self..
    you'll get the answer.
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  • Ankush Sharma

    Member • Dec 25, 2012

    bioramani
    What do you think makes water flow in a horizontal pipe. If you measure the inlet and out let pressure, you will find that the outlet pressure is less than the inlet. It is this differential that causes flow. If there is no differential water does not flow. In this case the pressure decreases because of pipe friction. This is included in the extended Bernoulli's equation.

    That is true only if the force remains smae. The whole issue is that the force is not the same.
    okk dear thanks, i understand it😀
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  • Ankush Sharma

    Member • Dec 25, 2012

    vikas reddy
    pressu
    pressure energy is a function of pressure.......
    primarily just move out of the basic definition of pressure i.e force per area
    think wisely that the condition "pressure is inversely proportional to area is valid only at constant force, but force is not a constant in moving liquid so you cannot apply your assumption in this case."
    dear thanks for ur explanation, i understand it. thanks 😀
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  • Saandeep Sreerambatla

    Member • Dec 25, 2012

    Great Explanations guys , when I first read this thread I kind of confused but was going through the reply from Bioramani and Vikas and my doubts are cleared.
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