The velocity of the water in the pipe at right is given by V1 = 0.5t m/s and V2 = 1.0t m/s, where t is in seconds. Determine the local acceleration (Eulerian temporal) at points (1) and (2). Is the average Eulerian convective acceleration between these two points negative, zero, or positive?

A) At point 1, local acceleration = 0.5 m/s²

At point 2, local acceleration = 1.0 m/s²

B) Average Eulerian convective acceleration over the two points in the cross section shown = 0.5 m/s²

This value is positive indicating an increase in velocity and acceleration kf the fluid as the cross sectional Area of flow reduces.

Explanation:

Local acceleration at those points is the instantaneous acceleration at those points and it is given as

a = dv/dt

At point 1, v₁ = 0.5 t

a₁ =dv₁/dt = 0.5 m/s²

At point 2, v₂ = 1.0 t

a₂ = dv₂/dt = 1.0 m/s²

b) Average Eulerian convective acceleration over the two points in the cross section shown = (change of velocity between the two points)/time

Change of velocity between the two points = v₂ - v₁ = 1.0t - 0.5t = 0.5 t

Time = t

Average acceleration = 0.5t/t = 0.5 m/s²

This value is positive indicating an increase in velocity and acceleration kf the fluid as the cross sectional Area of flow reduces.

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