Bernoulli's Eq: P1=P2 & Torricelli's Eq

In summary, Bernoulli's equation is a fundamental principle in fluid dynamics that describes the relationship between pressure, velocity, and elevation in a fluid flow. P1 = P2 is a simplified form of Bernoulli's equation that states the pressure at two points along a streamline in a fluid flow is equal. This allows for the calculation of fluid properties at different points in the flow using only pressure measurements. Bernoulli's equation is used in various practical applications, such as designing aircraft wings, calculating airspeed, and understanding blood flow. Torricelli's equation is a special case of Bernoulli's equation that applies to incompressible fluid flow through a small opening, and it is used in real-life scenarios to calculate velocities of
  • #1
bluejay27
68
3
When using Bernoulli's equation to describe fluid that is coming out from a spigot, why is it that P1 = P2 are the same? This cancellation will eventually lead to the Torricelli's equation.
 
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  • #2
In deriving Torricelli's theorem, both ends of the streamline are assumed to be at atmospheric pressure. (They are exposed to the atmosphere.)
 
  • #3
Isn't the pressure supposed to be internal pressure?
 
  • #4
bluejay27 said:
Isn't the pressure supposed to be internal pressure?
Yes, it's the pressure inside the fluid. At those points that pressure must match the external atmospheric pressure.
 

FAQ: Bernoulli's Eq: P1=P2 & Torricelli's Eq

1. What is Bernoulli's equation?

Bernoulli's equation is a fundamental principle in fluid dynamics that describes the relationship between pressure, velocity, and elevation in a fluid flow. It states that the total energy of a fluid remains constant along a streamline, meaning that as the velocity of the fluid increases, the pressure decreases.

2. What is the significance of P1 = P2 in Bernoulli's equation?

P1 = P2 is a simplified form of Bernoulli's equation that states that the pressure at two points along a streamline in a fluid flow is equal. This is significant because it allows for the calculation of fluid properties at different points in the flow using only pressure measurements.

3. How is Bernoulli's equation used in practical applications?

Bernoulli's equation is used in various practical applications, such as designing aircraft wings, calculating airspeed in a wind tunnel, and understanding the flow of blood in the human circulatory system. It is also used in hydraulic systems, such as water turbines and pumps, to determine the flow rate and pressure.

4. What is Torricelli's equation?

Torricelli's equation is a special case of Bernoulli's equation that applies to the flow of an incompressible fluid through a small opening in a container. It states that the velocity of the fluid exiting the opening is equal to the velocity of a freely falling body under the influence of gravity at the same height.

5. How is Torricelli's equation used in real-life scenarios?

Torricelli's equation is used in real-life scenarios, such as calculating the velocity of water flowing out of a small opening in a tank or the velocity of air exiting an air compressor. It is also useful in understanding the flow of liquids through pipes or nozzles, as well as in designing fountains and sprinkler systems.

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