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dime la respuesta correcta de este ejercicio 

The problem you've shared is related to fluid dynamics, specifically the laminar flow of a viscous crude oil through a cylindrical pipe. The exercise asks for the calculation of the viscosity of the crude oil, and from the image, we have the following key parameters:

- **Length of the pipe (L):** 8 meters
- **Radius of the pipe (r):** 3 centimeters (0.03 meters)
- **Velocity of the fluid (v) at 1 centimeter from the center:** 0.5 meters per second
- **Pressure difference (ΔP):** 400 pascals
- **The flow is laminar.**

To calculate the viscosity of the crude oil, we can use **Hagen-Poiseuille's law** for laminar flow in a cylindrical pipe:

\[
v(r) = \frac{\Delta P}{4 \eta L} (R^2 - r^2)
\]

Where:
- \( v(r) \) is the velocity of the fluid at a distance \( r \) from the center of the pipe,
- \( \Delta P \) is the pressure difference (400 Pa),
- \( \eta \) is the dynamic viscosity (what we want to find),
- \( L \) is the length of the pipe (8 m),
- \( R \) is the radius of the pipe (0.03 m),
- \( r \) is the distance from the center (in this case, 0.01 m).

We can rearrange this formula to solve for \( \eta \).

Let me calculate it for you.The dynamic viscosity (\( \eta \)) of the crude oil is approximately **0.02 Pa·s** (Pascal-seconds).

Would you like more details or have any further questions? Here are some related questions to consider:

1. What are the typical conditions for laminar flow to occur?
2. How does the viscosity of a fluid impact its flow rate in a pipe?
3. How is Hagen-Poiseuille's equation derived for laminar flow?
4. What factors could cause the flow to become turbulent instead of laminar?
5. How does the pressure difference affect the velocity profile of a fluid in a pipe?

**Tip:** For higher viscosity fluids, the flow tends to be slower, and a larger pressure difference is needed to achieve the same flow rate as a less viscous fluid.

En una planta de procesamiento de petróleo, un ingeniero está evaluando la eficiencia del flujo de un crudo viscoso a través de un conducto horizontal de 8 metros de longitud y 3 centímetros de radio. La velocidad del crudo a una distancia de 1 centímetro del centro del conducto es de 0.5 metros por segundo. La diferencia de presión entre los extremos del conducto es de 400 pascales. Calcula la viscosidad del crudo, sabiendo que el flujo es laminar.

This exercise involves calculating the viscosity of crude oil in a laminar flow through a cylindrical pipe. The pipe has a length of 8 meters, a radius of 3 centimeters, and a pressure difference of 400 Pascals. The velocity of the oil at 1 centimeter from the pipe's center is 0.5 meters per second. Learn how to apply Hagen-Poiseuille's law to solve for the viscosity.

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