Fluid Dynamics: Pressure, Velocity & Pipe Radius

In summary, the problem involves water flowing in a horizontal pipe with variable radius and no drag. At one point in the pipe with a radius of 5.0cm, the flow is .75 m/s at a pressure of 250 N/m^2. We need to determine the velocity and radius at a point where the pressure is 200 N/m^2. We can use Bernoulli's equation and the continuity equation to solve for these values.
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1.Water flows in a horizontal pipe with variable radius and which produces no drag. At one point in the pipe where the radius is 5.0cm, the flow is noted as .75 m/s at a pressure of 250 N/m^2. a) What is the velocity at a point in the pipe where the pressure is 200 N/m^2? b) What is the radius of the pipe at this point?


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Water flows in a horizontal pipe with variable radius and which produces no drag. At one point in the pipe where the radius is 5.0cm, the flow is noted as .75 m/s at a pressure of 250 N/m^2. a) What is the velocity at a point in the pipe where the pressure is 200 N/m^2? b) What is the radius of the pipe at this point?

Bernoulli's for an incompressible fluid:

[tex]P_1 + \frac{v^2_1}{2} = P_2 + \frac{v^2_2}{2}[/tex]

[tex]A_1 v_1 = A_2 v_2[/tex]

You can take over from here.
 
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Related to Fluid Dynamics: Pressure, Velocity & Pipe Radius

1. What is fluid dynamics?

Fluid dynamics is the study of how fluids, such as liquids and gases, behave and interact with their surroundings. It involves understanding how pressure, velocity, and other factors affect the movement and flow of fluids.

2. How does pressure affect fluid dynamics?

Pressure is a key factor in fluid dynamics as it determines the direction and speed of fluid flow. It is defined as the force exerted by a fluid per unit area and is influenced by factors such as fluid density and velocity.

3. How does velocity impact fluid dynamics?

Velocity is the rate of change of position of a fluid particle over time. It is a crucial factor in fluid dynamics as it affects the pressure, flow rate, and other properties of a fluid. Changes in velocity can also cause turbulence and affect fluid behavior.

4. What is the relationship between pipe radius and fluid dynamics?

The pipe radius, or diameter, is a significant factor in fluid dynamics as it determines the cross-sectional area available for fluid flow. A larger pipe radius allows for a greater volume of fluid to flow through, resulting in lower pressure and higher velocity.

5. How is fluid dynamics used in real-world applications?

Fluid dynamics has numerous practical applications in fields such as engineering, meteorology, and biology. It is used to design efficient pipes and pumps, predict weather patterns, and understand the behavior of fluids in the human body, among other things.

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