Question

The container shown in FIGURE EX14.12 is filled with oil. It is open to the atmosphere on
the left.
a. What is the pressure at point A?
b. What is the pressure difference between points A and B? Between points A and C?

Short answer

a) Total pressure = 106 kPa

b) the pressure difference is $$\begin{gathered} P_C-P_A=4263Pa \\ {P}_B-P_A=4263Pa \end{gathered}$$

Step-by-step solution

Part(a) Given information

The tank and points are given in figure below

Part(a) Step 2: Explanation

Calculate the pressure at point A

$P_A=h\rho g$

Substitute the given values, density of oil , ρ = 870 kg/m³
g= 9.81 m/s². h=0.5 m ( from the figure)
and calculate

$$\begin{gathered} =0.5\times 870\times 9.8 \\ =4263\mathrm{Pa} \end{gathered}$$

P_Total = P_atm + P_oil

P_Tota = 101325+4263 Pa=106 kPa

Part(b) Given information

The tanks details and points are given in the figure.

Part(b) Step2: Explanation

From the figure the depth at the points B and C is 1 m.

So the pressure at B and C is same

$$\begin{gathered} P_B=h\rho g \\ =1.0\times 870\times 9.8 \\ =8526\mathrm{Pa} \end{gathered}$$

$P_B=P_C=8526\mathrm{Pa}$

We have calculated in Part(a)

P_A = 4263 Pa

So

$P_B-P_A=8526-4263=4263Pa$

Similarly

$P_C-P_A=8526-4263=4263Pa$