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nal homogeneity The one dimensional Navier Stokes eqn takes the form dw dw w dz...

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nal homogeneity The one dimensional Navier Stokes eqn takes the form dw dw w dz t Cop dz 4 PO where w p P H g are the velocity pressure density viscosity and gravitational acceleration respectively t z are time and z coordinate which is chosen in the opposite direction of gravity Dimensional homogeneity of an equation requires each term in an equation having the same dimension 2 1 Express dimension of the coefficient C in terms of M L T 2 2 Verify that dimensional homogeneity is satisfied by the equation check each term and make sure they all have the same dimension

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