Fluid flowing in a sphere and leaving

In summary, the conversation discusses the flow rate of benzene and its dependence on the liquid's height. The equation in part c suggests that the flow rate changes with time, and this requires integration. Additionally, the equation for the volume of a not completely filled liquid is mentioned, but its accuracy is uncertain. The flow rate is always influenced by the current height due to the decrease in pressure at the bottom.
  • #1
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Homework Statement


Homework Equations


The Attempt at a Solution


Just checking if this is correct, and if the equation in part c implies that the flow rate out changes with time, or is just based off the initial height..I think it changes and therefore requires this integration. Also, I looked up the equation for the volume of a liquid that is not filled up, not sure if it is correct or not
 

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  • #2
The flow always depends on the current height, of course - benzene has no "memory" of some initial height. The physical reason for the height-dependence is the pressure at the bottom, which drops with a reduced height.
 

FAQ: Fluid flowing in a sphere and leaving

1. How does fluid flow in a sphere?

When fluid flows in a sphere, it follows a path known as a streamline. This means that the fluid particles move in a smooth and continuous manner, without crossing each other's paths. The direction of flow is determined by the pressure gradient in the fluid and the shape of the sphere.

2. What factors affect the flow of fluid in a sphere?

The flow of fluid in a sphere is affected by several factors, including the viscosity of the fluid, the velocity of the flow, the shape and size of the sphere, and the surface roughness of the sphere. These factors can influence the flow rate, turbulence, and pressure distribution within the sphere.

3. What happens when fluid leaves a sphere?

When fluid leaves a sphere, it creates a flow pattern known as a jet. This is because the fluid is forced to accelerate as it exits the narrow opening of the sphere. The shape of the jet is dependent on the speed and direction of the fluid leaving the sphere, as well as the surrounding conditions.

4. How does the flow of fluid in a sphere affect its properties?

The flow of fluid in a sphere can significantly impact its properties, such as pressure, temperature, and velocity. As the fluid flows through the sphere, it can experience changes in these properties due to the forces and interactions between the fluid particles and the spherical surface. Understanding these changes is crucial for various industrial and scientific applications.

5. What are some real-world applications of fluid flow in a sphere?

The study of fluid flow in a sphere has many practical applications, including in meteorology, aerospace engineering, and hydrodynamics. It is also essential in understanding natural phenomena such as ocean currents, cloud formation, and blood flow in the human body. Additionally, this knowledge is crucial for designing and optimizing various systems, such as pumps, turbines, and pipelines.

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