The fluid flow discussion focuses on the dynamic pressure difference
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Dear seniors: I have a question: Regarding the relationship between pressure and flow rate inside a pipe after it has its diameter changed, this can be calculated using Bernoulli’s equation, namely p + 1/2ρv^2 + ρgh = C (where p, ρ, and v represent the pressure, density, and velocity of the fluid, respectively)； h is the vertical height ； (g is the acceleration due to gravity.) The various terms in the above equation represent, respectively, the pressure energy per unit volume of fluid, p; the gravitational potential energy, ρg h; and the kinetic energy, (1/2)*ρv^2. As the fluid moves along the flow lines, the sum of these values remains constant, which is the principle of conservation of total energy. For pipelines with a change in diameter in the horizontal straight section: according to mass balance, the flow rate remains unchanged after the diameter changes ； According to Bernoulli’s equation, if the pipe diameter increases from small to large, the flow velocity decreases while the pressure increases ； If the pipe diameter decreases: the flow velocity increases, and the pressure decreases. What I’m confused about now is this: based on the above reasoning, as the pipe diameter increases from small to large, the pressure increases; will the fluid flow in reverse direction (from where the pressure is high to where it is low)? I would appreciate some guidance from those with experience in this field. Thank you! However, the total energy between different streamlines (i.e., the constant value in the above equation) may vary. For gases, gravity can be ignored, and the equation simplifies to p + (1/2)*ρv^2 = constant (p0); these terms are referred to as static pressure, dynamic pressure, and total pressure respectively. Obviously, as the velocity increases in flow, the pressure decreases ； As the speed decreases, the pressure increases ； When the velocity drops to zero, the pressure reaches its maximum value (theoretically equal to the total pressure).
Dear seniors: I have a question: Regarding the relationship between pressure and flow rate inside a pipe after it has its diameter changed, this can be calculated using Bernoulli’s equation, namely p + 1/2ρv^2 + ρgh = C (where p, ρ, and v represent the pressure, density, and velocity of the fluid, respectively)； h is the vertical height ； (g is the acceleration due to gravity.) The various terms in the above equation represent, respectively, the pressure energy per unit volume of fluid, p; the gravitational potential energy, ρg h; and the kinetic energy, (1/2)*ρv^2. As the fluid moves along the flow lines, the sum of these values remains constant, which is the principle of conservation of total energy. For pipelines with a change in diameter in the horizontal straight section: according to mass balance, the flow rate remains unchanged after the diameter changes ； According to Bernoulli’s equation, if the pipe diameter increases from small to large, the flow velocity decreases while the pressure increases ； If the pipe diameter decreases: the flow velocity increases, and the pressure decreases. What I’m confused about now is this: based on the above reasoning, as the pipe diameter increases from small to large, the pressure increases; will the fluid flow in reverse direction (from where the pressure is high to where it is low)? I would appreciate some guidance from those with experience in this field. Thank you!
The original poster should study the Bernoulli equation more carefully – there’s also pipe friction on both sides; why didn’t you take that into account? Look at the example below; do you understand?
I think the backflow you deduced is correct, but the result of this backflow isn’t the liquid flowing backward as you thought; rather, boundary layer separation occurs, generating vortices. The result of eddy currents is the local resistance loss mentioned above.
What the original poster meant by “getting larger” and “getting smaller” refers to trends in change; after the pipe is expanded, the flow velocity (v2) decreases, while the pressure (P2) increases. However, the pressure does not become greater than the initial driving force (P1)!
If, through diameter expansion, P2 becomes larger than P1, then a Nobel Prize can be won, because a perpetual motion machine has been created! ;P;P