Why Is Pressure in Fluids Considered Perpendicular to Surfaces?

[sumit saurav]

why the forces in pressure always taken perpendicular?
and if they are taken then to which direction?
and what about presure on a curved plane?

 

[Mentz114]

If a ball bounces off a wall with a perfect elastic collision then the change of momentum of the ball is perpendicular to the wall at the point of collision. Thus the force exerted on the wall is perpendicular to the wall. In a simple mechanical model pressure is the force resulting from many such collisions by gas atoms or molecules with random angles of incidence.

 

[sumit saurav]

how does it explains us taking perpendicular direction as

 

[Chestermiller]

how does it explains us taking perpendicular direction as

Are you familiar with the concept that pressure is an isotropic tensor?

Chet

 

[sumit saurav]

nope could you explain?

 

[Chestermiller]

nope could you explain?

We usually start out by learning that pressure is force per unit area, and is a scalar. As we progress, we later learn that pressure is not a scalar, but actually a tensorial quantity, equal to the isotropic (not direction-dependent) part of the more general stress tensor. We sometimes use matrix notation to describe the components of a tensor. For any orthogonal coordinate system, the pressure portion of the stress tensor is represented by:
$$\left(\begin {array}{ccc}p&0&0\\0&p&0\\0&0&p\end {array}\right)$$
We can obtain the pressure force per unit area acting on a surface oriented in an arbitrary direction in space by dotting the pressure tensor with a unit normal to the surface:
$$\left(\begin {array}{ccc}p&0&0\\0&p&0\\0&0&p\end {array}\right)\left(\begin {array}{c}n_x\\n_y\\n_z\end{array}\right)=\left(\begin {array}{c}pn_x\\pn_y\\pn_z\end{array}\right)=p\left(\begin {array}{c}n_x\\n_y\\n_z\end{array}\right)$$
Note that, with this mathematical representation, the pressure force per unit area is automatically delivered as a vector with magnitude p and direction normal to the surface.

Chet