Question

3. An iron cube (e-7860 kg/m) having sides of 1 cm is submerged in open fresh water (p = 1000

kg/m with its top surface at a depth of 2.5 m. Considering that its top surface is held horizontal
with respect to the water surface, determine the difference in pressure between the top and
bottom surfaces of the cube?​

Answer 1

98 Pa

Step-by-step explanation:

Given that:

The density
`\rho` of the iron cube = 7860 kg/m

side of the iron cube = 1 cm = 0.01 m

density of the open fresh water
`\rho` = 1000 kg/m

depth of the top surface = 2.5 m

the difference in pressure between the top and bottom surfaces of the cube is determined by the hydrostatic condition;

`\Delta P = P_(bottom) - P_(top)`

where

`P_(bottom) = pgh \\ \\ P_(bottom) = 1000*9.8*(2.5+0.01) \\ \\ P_(bottom) = 24598 \ Pa`

`P_(top) = pgh \\ \\ P_(top) = 1000*9.8*2.5 \\ \\ P_(top) =24500 \ Pa`

`\Delta P = P_(bottom) - P_(top)`

`\Delta P =24598 - 24500`

`\Delta P =98 \ Pa`

the difference in pressure between the top and bottom surfaces of the cube is 98 Pa