# Fluid Viscosity

In the derivation of Bernoulli’s equation, the assumption of the inviscid and incompressible flow is used. However in the real case, the viscosity cannot be neglect and the density of the flow is not always constant. Thus Bernoulli’s equation is not always correct. For the lab, it is reasonable to assume the flow is inviscid and incompressible. Firstly, the pitot was placed at the center of the flow. The skin friction (effect of viscosity) is inversely proportional to distance. Therefore the effect of viscosity can be neglected in the pitot. Secondly, the speed of the flow is much lower than the speed of sound under the sonic condition. Therefore, the Mach number is low enough to neglect the change of density of the controlled volume and the controlled volume is almost incompressible. That is why we can estimate the velocity of the flow by Bernoulli’s equation and continuity equation.

As a result of the viscosity, the internal flow is constrained by the bounding walls and the effect grows during the entire flow. At the inflow region, the flow is nearly inviscid. After that, the boundary layers are growing along the duct which is called developing profile region. This is because the effect of viscosity is growing. At the centre of the duct, there is an inviscid core flow. When the boundary layers are merged, the flow is fully developed and the velocity is not affected by viscosity anymore. Meanwhile the static pressure decreases due to the effect of viscosity (friction). The expanding area of diffuser produces low velocity, which increases the pressure and adverse gradient. The fluid is viscid and the boundary layer is separated as a result of the back flow and poor pressure recovery, if the angle is large. The separation will increase the flow losses. Besides, the larger angle leads to the earlier separation and heavier flow losses. If there is an abrupt enlargement, because of viscosity, large vortex flow causes the flow losses and...

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