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(a) Consider a container of fluid subject to a vertical upward acceleration a. Show that the pressure variation with depth in the fluid is given by P = ph(g + a), Where h is the depth and p is thee density. (b) Show also that if the fluid as a whole undergoes a vertical downward acceleration a, the pressure at depth h is given by P = ph(g – a),

(a) Consider a container of fluid subject to a vertical upward acceleration a. Show that the pressure variation with depth in the fluid is given by
P = ph(g + a),
Where h is the depth and p is thee density. (b) Show also that if the fluid as a whole undergoes a vertical downward acceleration a, the pressure at depth h is given by
P = ph(g – a),

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
6 years ago
(a) It is given that the container is moving vertically upward with an acceleration .So, it can be considered that the fluid in the container is also having the same acceleration.
Let us consider a slice of cross sectional area A of the fluid at a depth h from the surface.
233-549_1.PNG
The mass of the fluid above the slice is
233-550_1.PNG
233-832_1.PNG
233-1888_1.PNG

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