For the speed equation along centerline of a diffuser, calculate the fluid acceleration along the diffuser centerline as a function of x and the given parameters. For L = 1.56 m, uentrance = 24.5 m/s, and uexit = 17.5 m/s, calculate the acceleration at x = 0 and x = 1.0 m.

, ,

Explanation:

Let suppose that fluid is incompressible and diffuser works at steady state. A diffuser reduces velocity at the expense of pressure, which can be modelled by using the Principle of Mass Conservation:

The following relation are found:

The new relationship is determined by means of linear interpolation:

After some algebraic manipulation, the following for the velocity as a function of position is obtained hereafter:

The acceleration can be calculated by using the following derivative:

The derivative of the velocity in terms of position is:

The expression for acceleration is derived by replacing each variable and simplifying the resultant formula.

answer:

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