Bernoulli's Equation Pressure at Blockage

In summary, Bernoulli's equation is a fundamental principle in fluid dynamics that states the total energy of a fluid remains constant in a closed system and can be used to calculate changes in pressure at blockages. According to this equation, pressure decreases as velocity increases, and the size and shape of a blockage can affect this change in pressure. However, the equation is not always accurate and is best used for simple blockages. It has various practical applications in engineering and science fields, such as designing efficient pipelines and understanding the flow of air and water in pipes and channels.
  • #1
quark002
3
0
Homework Statement
Bernoulli's equation tells us that a portion of a stream that is slower-moving has a higher pressure than a portion of the same stream that is faster-moving. What would happen if I blocked the flow of two different streams, a faster-moving stream and a slower-moving stream? Why would I experience a higher pressure when blocking the faster-moving stream?
Relevant Equations
$$\frac{p}{\rho} + \frac{v^2}{2} = \text{cst}$$
Would it be because I'm comparing two different streams as opposed to two portions of the same stream?
 
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  • #2
Can you please describe this system in more detail, with a diagram.
 
  • #3
quark002 said:
if I blocked the flow of two different streams, a faster-moving stream and a slower-moving stream?
If there are two different streams there is no relationship between their pressures. You could add a constant pressure throughout one of the streams and nothing would change in the flow.
 

1. What is Bernoulli's equation?

Bernoulli's equation is an equation that describes the relationship between pressure, velocity, and elevation of a fluid in a steady flow. It states that as the velocity of a fluid increases, the pressure decreases, and vice versa.

2. How is Bernoulli's equation used to calculate pressure at blockage?

Bernoulli's equation can be used to calculate the pressure at blockage by using the continuity equation, which states that the mass flow rate is constant throughout a fluid system. By rearranging the equation, the pressure at blockage can be calculated using the known velocity and density of the fluid.

3. What is blockage in relation to Bernoulli's equation?

Blockage in relation to Bernoulli's equation refers to an obstruction or narrowing in the flow of a fluid. This can occur due to the presence of a solid object or a change in the shape of the conduit through which the fluid is flowing.

4. How does blockage affect the pressure in a fluid system?

Blockage can affect the pressure in a fluid system by causing an increase in velocity and a decrease in pressure. This is due to the conservation of mass and energy, where the fluid must flow faster through a narrower area to maintain the same mass flow rate, resulting in a decrease in pressure.

5. What are some real-world applications of Bernoulli's equation for pressure at blockage?

Bernoulli's equation for pressure at blockage has numerous applications in various fields. Some examples include calculating the pressure drop in a pipe due to blockage, determining the airspeed of an aircraft, or predicting the flow rate through a nozzle or venturi meter.

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