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Why do we need to assume constant viscosity for a flowing fluid system when using the...

Why do we need to assume constant viscosity for a flowing fluid system when using the equations for momentum balances, since viscosity term is already outside the partial differential sign/ function.

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in fluid flowing system we assume that viscosity is only dependent on temperature. In momentum balance of flowing fluid the change in viscosity along the axial direction of the pipe is too much small. there is small change in viscosity when fluid flows from one end to another. so the viscosity of fluid is considered to be constant throughout the flow. and not used as a partial difference function.

another factor is we mostly considered newtonion fluid in momentum balance which have constant viscosity.

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