Force Acting on Area: ucos(theta)dA vs usin(theta)dA

In summary, ucos(theta)dA and usin(theta)dA are both used to calculate the force acting on an area, but they differ in terms of direction. Ucos(theta)dA represents a force perpendicular to the surface, while usin(theta)dA represents a force parallel to the surface. The direction of the force can be determined by the angle theta, with 90 degrees representing a perpendicular force and 0 degrees representing a parallel force. These expressions can be used for any type of force and are directly related to the concept of pressure. The value of ucos(theta)dA and usin(theta)dA will vary depending on the size of the area, but the direction of the force will remain the same.
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foo9008
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Homework Statement


dA lies on x and y aixs , right ? the author gave that the volume flow rate thru element A is ucos(theta)dA , why not
usin(theta)dA ? if u ' = ucos(theta) , it will become parallel to dA , right ? since u' will be parallel to x-axis...

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dA is in the yz plane
 
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FAQ: Force Acting on Area: ucos(theta)dA vs usin(theta)dA

What is the difference between ucos(theta)dA and usin(theta)dA?

Both ucos(theta)dA and usin(theta)dA are expressions used to calculate the force acting on an area. The main difference between them is the direction of the force. Ucos(theta)dA represents a force acting perpendicular to the surface, while usin(theta)dA represents a force acting parallel to the surface, with theta being the angle between the force and the normal of the surface.

How do you determine the direction of the force using ucos(theta)dA and usin(theta)dA?

The direction of the force can be determined by the angle theta. If theta is 90 degrees, the force will be acting perpendicular to the surface (ucos(theta)dA). If theta is 0 degrees, the force will be acting parallel to the surface (usin(theta)dA).

Can these expressions be used for any type of force?

Yes, ucos(theta)dA and usin(theta)dA can be used for any type of force as long as it is acting on a specific area. This includes both gravitational and electromagnetic forces.

How do these expressions relate to the concept of pressure?

Pressure is defined as the force per unit area. In the case of ucos(theta)dA and usin(theta)dA, the force is calculated for a specific area. Therefore, these expressions are directly related to the concept of pressure.

Is the value of ucos(theta)dA or usin(theta)dA affected by the size of the area?

Yes, the value of ucos(theta)dA and usin(theta)dA will vary depending on the size of the area. As the area increases, the force acting on that area will also increase. However, the direction of the force will remain the same.

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