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Forces in fluid or pressure
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[QUOTE="Chestermiller, post: 4624073, member: 345636"] 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 [I]stress tensor[/I]. 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: [tex]\left(\begin {array}{ccc}p&0&0\\0&p&0\\0&0&p\end {array}\right)[/tex] 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: [tex]\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)[/tex] 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 [/QUOTE]
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