Velocity of fluid through a spherical surface

In summary, the speed at which the fluid passes through the plane is equal to the dot product of the velocity vector and the unit normal vector to the plane.
  • #1
racnna
40
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Fluid flows with velocity 2i - 3j m/s at point P having coordinates (1,2,4). Consider a plane through P which is normal to the vector b=-i+2k. What is the speed at which the fluid passes through the plane?

Should I do the dot product of the position vector P=[1,2,4] and b vector, then multiply this by unit vector that is in the direction of the b vector, and then dot the result with the velocity vector?? i did this and got a negative velocity! HELP
 
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  • #2
racnna said:
Fluid flows with velocity 2i - 3j m/s at point P having coordinates (1,2,4). Consider a plane through P which is normal to the vector b=-i+2k. What is the speed at which the fluid passes through the plane?

Should I do the dot product of the position vector P=[1,2,4] and b vector, then multiply this by unit vector that is in the direction of the b vector, and then dot the result with the velocity vector?? i did this and got a negative velocity! HELP

The volumetric flux of fluid (volume per unit area = normal component of velocity) is equal to the velocity dotted with a unit normal to the plane.
 

FAQ: Velocity of fluid through a spherical surface

What is the velocity of fluid through a spherical surface?

The velocity of fluid through a spherical surface is the rate at which the fluid is flowing through the surface. It is usually measured in units of meters per second (m/s) or feet per second (ft/s).

How is the velocity of fluid through a spherical surface calculated?

The velocity of fluid through a spherical surface can be calculated using the equation v = Q/A, where Q is the flow rate of the fluid through the surface and A is the surface area of the sphere.

What factors affect the velocity of fluid through a spherical surface?

The velocity of fluid through a spherical surface can be affected by several factors, including the pressure of the fluid, the viscosity of the fluid, and the diameter of the spherical surface. Other factors such as the shape of the surface and the density of the fluid can also play a role.

How does the velocity of fluid through a spherical surface affect the flow of the fluid?

The velocity of fluid through a spherical surface is directly related to the flow rate of the fluid. As the velocity increases, the flow rate also increases. Additionally, the velocity can also affect the turbulence and pressure of the fluid flow through the surface.

What are the practical applications of understanding the velocity of fluid through a spherical surface?

Understanding the velocity of fluid through a spherical surface is important in many industries, such as engineering, hydrology, and aerodynamics. It can help in designing efficient pipelines, predicting the flow of water in rivers and streams, and designing aerodynamic structures for airplanes. It is also important in understanding the behavior of fluids in various systems and processes.

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