Question

If a vessel containing a fluid of density rho up to height H is accelerated vertically downward with acceleration a note then the pressure by fluid the bottom of vessel is

Answer 1

Explanation:

pressure at bottom

p = rho× H × g.

Answer 2

The pressure by fluid the bottom of vessel is $\rho \times (g-a)\times H$.

Explanation:

1. Given

   density of fluid =$\rho (\frac{kg}{m^{3}})$

   Height of fluid = H (m)

   Let area of base of vessel = A $(m^{2})$

   mass of fluid (M) = $\rho \times A\times H$   (kg)      ...1)

2. Acceleration due to gravity = $g (\frac{m}{s^{2}})$

   Where vessel is accelerated in downward direction =  $a (\frac{m}{s^{2}})$

3. From D' Alembert equation

   Net downward force = Mg- Ma= M(g-a)       ...2)

4.  Now

    Pressure on bottom of vessel $P= \frac{Net downwardforce}{Area}$    ...3)

    $P= \frac{\rho \times A\times H\times (g-a)}{A}$

    So

    Pressure on bottom of vessel  $(P)=\rho \times (g-a)\times H$