A cubical box has 20 CM on a side is completely immersed in a fluid At the top of the box the pressure is 105kpa and at the bottom the pressure is 106point8kpa What is the density of the fluid guees the fluid
Answers
If a cubical box of 20 cm is immersed in a fluid then the density of the fluid is 920 kg/m³ and the fluid may be a cooking oil (Olive oil).
Explanation:
Required formula:
The pressure of the fluid at some depth is given by = ρgh …… (i)
Step 1:
The side of the cubical box = 20 cm = 0.2 m
The pressure at the top of the box = 105 kPa = 105 * 10³ Pa
The pressure at the bottom of the box = 106.8 kPa = 106.8 * 10³ Pa
From the figure (1) attached below, we can assume that the level of the fluid starts from some height above the top of the cubical box, so, let
The depth of the fluid till the top of the box be denoted as “d1”.
And, the depth of the fluid till the bottom of the box be denoted as “d2”.
Step 2:
Therefore, based on the formula (i), we get
The pressure at the top “Pt” of the box will be = ρgd1
⇒ 105*10³ = ρgd1 ……. (ii)
And,
The pressure at the bottom “Pb” of the box will be = ρgd2
⇒ 106.8*10³ = ρgd2……. (iii)
By subtracting (ii) from (iii), we get
106.8*10³ - 105*10³ = ρgd2 - ρgd1
⇒ 1.8 * 10³ = ρg [d2 – d1]
Taking g = 9.8 m/s² and from the figure d2 – d1 = length of the side of the cubical box = 0.2 m
⇒ 1.8 * 10³ = ρ* 9.8 * 0.2
⇒ ρ = [1.8 * 10³] / [1.96]
⇒ ρ = [1.8 * 10³] / [1.96]
⇒ ρ = 918.36 kg/m³
From the figure (2) attached below we can see that the density of cooking oil is between 910 - 930 kg/m³ and density of olive oil is 910 kg/m³ ∴ the fluid can be olive oil.
Thus, the density of the fluid is 918.36 kg/m³ and the fluid can be Olive oil.
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