A fluid particle flowing along a stagnation streamline, as shown in Video V4.9 and Fig. P4.38, slows down as it approaches the stagnation point. Measurements of the dye flow in the video indicate that the location of a particle starting on the stagnation streamline a distance \(s=0.6 \mathrm{ft}\) upstream of the stagnation point at \(t=0\) is given approximately by \(s=0.6 e^{-0.5 t}\), where \(t\) is in seconds and \(s\) is in feet.

(a) Determine the speed of a fluid particle as a function of time, \(V_{\text {particle }}(t)\), as it flows along the streamline.

(b) Determine the speed of the fluid as a function of position along the streamline, \(V=V(s)\).

(c) Determine the fluid acceleration along the streamline as a function of position, \(a_{s}=a_{s}(s)\).

Figure P4.38 

Transcribed Image Text:

Stagnation point, x = 0 Fluid particle V