basic laws in Fluid Mechanics

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The first term is the unsteady term, which would go to zero in cases where the flow is steady (does not change with time) or when the flow is incompressible (density of fluid is constant). The second term refers to the sum of the mass flow rates leaving the control volume through the surface ‘j’. The third term is the sum of the mass flow rates entering the control volume through ‘k’. Volumetric flow rate is given by the product of the flow area and the velocity of flow, i.e. Q = Av, where Q is the volumetric flow rate, in m3/s, A is the cross sectional area of flow, in m2 and v is the average velocity of the fluid normal to the surface in m/s. In general, if the velocity varies with the flow area, then we can write Q= ∫v.dA (integrated over the surface, A) An incompressible fluid flows steadily over an impermeable (no flow can pass through) flat plate as in the Figure below. The height of the control volume is δ. The inlet velocity is uniform, i.e. v= U o and the exit velocity profile is a cubic polynomial given by: u where, δ η y. Compute the volumetric flow rate across the top surface of the control volume.