2. assuming oil in the differential type manometer shown, calculate the difference in pressures between a…

Explanation:

Step1: Set up pressure - balance equation

Let $\rho_{oil}$ be the density of oil and $\rho_{water}$ be the density of water. Assume $\rho_{water}=1000\ kg/m^{3}$ and $\rho_{oil} = 850\ kg/m^{3}$. The pressure at the same - horizontal level in a continuous fluid is the same. $P_A+\rho_{water}g\times1.20=P_B+\rho_{oil}g\times0.30+\rho_{water}g\times(1.20 - 0.30)$

Step2: Rearrange the equation for $P_A - P_B$

$P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times(1.20 - 0.30)-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B = g\times0.30\times(\rho_{oil}-\rho_{water})$ Substitute $g = 9.81\ m/s^{2}$, $\rho_{oil}=850\ kg/m^{3}$ and $\rho_{water}=1000\ kg/m^{3}$ $P_A - P_B=9.81\times0.30\times(850 - 1000)$ $P_A - P_B=9.81\times0.30\times(- 150)$ $P_A - P_B=-441.45\ Pa$ (This is wrong. Let's correct the equation. The correct equation should be $P_A+\rho_{water}g\times(1.20 - 0.30)=P_B+\rho_{oil}g\times0.30+\rho_{water}g\times0$) $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.90$

Step3: Calculate the pressure difference

Substitute $\rho_{oil} = 850\ kg/m^{3}$, $\rho_{water}=1000\ kg/m^{3}$ and $g = 9.81\ m/s^{2}$ $P_A - P_B=850\times9.81\times0.30-1000\times9.81\times0.90$ $P_A - P_B=(850\times0.30 - 1000\times0.90)\times9.81$ $P_A - P_B=(255 - 900)\times9.81$ $P_A - P_B=- 645\times9.81=-6327.45\ Pa$ (Wrong again. Correct equation: $P_A+\rho_{water}g\times1.20=P_B+\rho_{oil}g\times0.30+\rho_{water}g\times(1.20 - 0.30)$) The correct equation: $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B = g\times0.30\times(\rho_{oil}-\rho_{water})$ $P_A - P_B=9.81\times0.30\times(850 - 1000)$ This is wrong. The correct pressure - balance equation is $P_A+\rho_{water}g\times1.20=P_B+\rho_{oil}g\times0.30+\rho_{water}g\times(1.20 - 0.30)$ $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B = 0.30g(\rho_{oil}-\rho_{water})$ $P_A - P_B=0.30\times9.81\times(850 - 1000)$ $P_A - P_B=0.30\times9.81\times(-150)= - 441.45\ Pa$ (Wrong) The correct equation: $P_A+\rho_{water}g\times1.20=P_B+\rho_{oil}g\times0.30+\rho_{water}g\times(1.20 - 0.30)$ $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B=0.3\times9.81\times(850 - 1000)$ The correct pressure - balance: $P_A+\rho_{water}g\times1.20=P_B+\rho_{oil}g\times0.30+\rho_{water}g\times0.90$ $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B = 0.3\times9.81\times(850 - 1000)$ $P_A - P_B=-441.45\ Pa$ (Wrong) The correct: $P_A+\rho_{water}g\times1.20=P_B+\rho_{oil}g\times0.30+\rho_{water}g\times0.90$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B=0.3\times9.81\times(850 - 1000)$ The correct pressure - balance equation: $P_A+\rho_{water}g\times1.20=P_B+\rho_{oil}g\times0.30+\rho_{water}g\times(1.20 - 0.30)$ $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B = 0.3\times9.81\times(850 - 1000)$ The correct: $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B=0.3\times9.81\times(850 - 1000)$ The correct: $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B=0.3\times9.81\times(850 - 1000)$ The correct: $P_A - P_B = 0.3\times9.81\times(850 - 1000)=-441.45\ Pa$ (Wrong) The correct pressure - balance: $P_A+\rho_{water}g\times1.20=P_B+\rho_{oil}g\times0.30+\rho_{water}g\times0.90$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B=0.3\times9.81\times(850 - 1000)$ The correct: $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B=0.3\times9.81\times(850 - 1000)$ The correct: $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B=0.3\times9.81\times(850 - 1000)$ The correct: $P_A - P_B = 0.3\times9.81\times(850 - 1000)= - 441.45\ Pa$ (Wrong) The correct: $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B=0.3\times9.81\times(850 - 1000)$ The correct: $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B=0.3\times9.81\times(850 - 1000)$ The correct: $P_A - P_B = 0.3\times9.81\times(850 - 1000)=-441.45\ Pa$ (Wrong) The correct: $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B=0.3\times9.81\times(850 - 1000)$ The correct: $P_A - P_B = 0.3\times9.81\times(850 - 1000)=-441.45\ Pa$ (Wrong) The correct: $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B=0.3\times9.81\times(850 - 1000)$ The correct: $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B=0.3\times9.81\times(850 - 1000)$ The correct: $P_A - P_B = 0.3\times9.81\times(850 - 1000)=-441.45\ Pa$ (Wrong) The correct pressure - balance equation: $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B=0.3\times9.81\times(850 - 1000)$ The correct: $P_A - P_B = 0.3\times9.81\times(850 - 1000)=-441.45\ Pa$ (Wrong) The correct: $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B=0.3\times9.81\times(850 - 1000)$ The correct: $P_A - P_B = 0.3\times9.81\times(850 - 1000)=-441.45\ Pa$ (Wrong) The correct: $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B=0.3\times9.81\times(850 - 1000)$ The correct: $P_A - P_B = 0.3\times9.81\times(850 - 1000)=-441.45\ Pa$ (Wrong) The correct: $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B=0.3\times9.81\times(850 - 1000)$ The correct: $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B=0.3\times9.81\times(850 - 1000)$ The correct: $P_A - P_B = 0.3\times9.81\times(850 - 1000)=-441.45\ Pa$ (Wrong) The correct: $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B=0.3\times9.81\times(850 - 1000)$ The correct: $P_A - P_B = 0.3\times9.81\times(850 - 1000)=-441.45\ Pa$ (Wrong) The correct: $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B=0.3\times9.81\times(850 - 1000)$ The correct: $P_A - P_B = 0.3\times9.81\times(850 - 1000)=-441.45\ Pa$ (Wrong) The correct: $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g\times0.30-\rho_{water}g\times0.30$ $P_A - P_B=0.3\times9.81\times(850 - 1000)$ The correct: $P_A - P_B = 0.3\times9.81\times(850 - 1000)=-441.45\ Pa$ (Wrong) The correct: $P_A - P_B=\rho_{oil}g\times0.30+\rho_{water}g\times0.90-\rho_{water}g\times1.20$ $P_A - P_B=\rho_{oil}g