First slide

Pressure in a fluid-mechanical properties of fluids

Question

An isosceles triangular plates of base 3 m and altitude 3 m is immersed in oil vertically with its base coinciding with the free surface of the oil of relative density 0.8. Determine the total thrust.

Moderate

A

24 kN
B

48 kN
C

36 kN
D

none of these

Solution

$Area of the plate = 1 / 2 \times base \times altitude$
$= 1 / 2 \times 3 \times 3 = 4.5 m^{2}$
$Density of oil = 0.8 \times 1000 = 800 {kgm}^{- 3} Depth of c.g. of the plate from the free surface = \frac{h}{3} = (1 / 3) 3 = 1 m$
$P r e s s u r e a t C O M o f p l a t e = ρ g (\frac{h}{3}) = (800 \times 10 \times 1) P a$
Net thrust force acts at center of mass of plate.
$Now, total thrust on the plate = (plate area) \times (pressure at the c.g. of the plate)$
$= (4.5) (800 \times 10 \times 1) = 36 kN$

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