What are the differences between Difference between Continuity vs Bernoulli vs Poiseuille's equation?

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lotus0618
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What are the differences between Difference between Continuity vs Bernoulli vs Poiseuille's equation?

Post by lotus0618 » Fri Jul 10, 2020 9:19 pm

What are the differences between Difference between Continuity vs Bernoulli vs Poiseuille's equation? thanks
NS_Tutor_Yuqi
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Joined: Fri May 29, 2020 11:43 pm

Re: What are the differences between Difference between Continuity vs Bernoulli vs Poiseuille's equation?

Post by NS_Tutor_Yuqi » Sun Jul 12, 2020 2:28 pm

Continuity Equation: Q=A1V1=A2V2. Q is the flow rate, A is the cross sectional area, v is the linear speed of the fluid. This is essentially saying that flow rate is remains constant within a closed system, even if the area changes. Therefore, the fluid will flow faster through narrow passages and slower through wide passages. You use this equation to determine how the area or velocity changes as you move through a closed system.

Poiseuille's Law: Q=(pi*r^4*P)/(8nL). This equation allows us to calculate Q, or flow rate, when there is laminar flow. As opposed to the continuity equation, which is comparing two points in one system, this one allows you to calculate the relationship between a bunch of different variables, such as radius, pressure gradient, viscosity, and length of the pipe. However, you usually won't be using this equation to solve for a specific value, but rather to determine the effects of changing one variable. For example, if radius increases by a factor of 2, then flow rate increases by a factor of 16.

Bernoulli's Equation: This equation looks pretty complex, but becomes rather simple once you break it down. It's essentially saying that the sum of the dynamic pressure and the static pressure within a closed system will be constant for fluids that cannot be compressed. This can be applied to the Venturi flow meter, which is a tube that has varying cross sectional areas. When the tube narrows, the linear speed increases, and therefore the pressure decreases.
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