Anozzle is designed to accelerate the fluid from v1 to v2 in a linear fashion. that is, v = ax + b, where a and b are constants. if the flow is constant with v1 = 10 m/s at x1 = 0 and v2 = 25 m/s at x2 = 1 m, determine (a) the local acceleration; (b) the acceleration magnitude of the fluid at point (1); (c) the acceleration magnitude of the fluid at point (2).

Explanation:

v = ax + b

when x = 0 , v = 10 ( given )

10 = b

when x = 1 , v = 25

25 = a + b

25 = a + 10

a = 15

So

v = 15 x + 10

acceleration

v = 15 x + 10

differentiating it on both sides wrt t

a = dv / dt = 15 dx / dt

a = 15 v = 15 ( 15x + 10 )

a = 225x + 150

acceleration at x = 0

a = 150 m/s²

acceleration at x = 1 m

a = 225 + 150

= 375 m /s²

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