A U-tube differential manometer connects two pipes A and B. The pipe A contains carbon tetrachloride having a specific gravity 1.2 under a pressure of 120 KPa. The pipe B contains oil of specific gravity of 0.65 under a pressure of 200 KPa. The pipe A lies 2.5 m above pipe B. Find the difference of pressure measured by mercury as fluid filling U-tube.

To solve this problem, we need to calculate the pressure at the same level in both pipes and then find the difference.

Step 1: Calculate the pressure at the bottom of pipe A.

The pressure at the bottom of pipe A is the pressure at the top plus the pressure due to the column of carbon tetrachloride.

P_A_bottom = P_A_top + ρ_CCl4 * g * h

where:

• P_A_top is the pressure at the top of pipe A (120 KPa)
• ρ_CCl4 is the density of carbon tetrachloride, which can be calculated from its specific gravity (1.2) by multiplying it by the density of water (1000 kg/m^3), so ρ_CCl4 = 1.2 * 1000 = 1200 kg/m^3
• g is the acceleration due to gravity (9.81 m/s^2)
• h is the height of the column of carbon tetrachloride (2.5 m)

So, P_A_bottom = 120 KPa + 1200 kg/m^3 * 9.81 m/s^2 * 2.5 m = 147.3 KPa

Step 2: Calculate the pressure at the bottom of pipe B.

The pressure at the bottom of pipe B is just the pressure at the top, because there is no column of fluid above it.

P_B_bottom = P_B_top = 200 KPa

Step 3: Calculate the difference in pressure.

ΔP = P_B_bottom - P_A_bottom = 200 KPa - 147.3 KPa = 52.7 KPa

So, the difference in pressure measured by the mercury in the U-tube manometer is 52.7 KPa.

To solve this problem, we need to calculate the pressure at the same level in the U-tube for both pipes and then find the difference.

Step 1: Calculate the pressure at the bottom of pipe A.

The pressure at the bottom of pipe A is the pressure at the top plus the pressure due to the column of carbon tetrachloride.

P_A_bottom = P_A_top + ρ_CCl4 * g * h

where:

• P_A_top is the pressure at the top of pipe A (120 KPa)
• ρ_CCl4 is the density of carbon tetrachloride, which can be found by multiplying the specific gravity by the density of water (1000 kg/m^3), so ρ_CCl4 = 1.2 * 1000 = 1200 kg/m^3
• g is the acceleration due to gravity (9.81 m/s^2)
• h is the height of the column of carbon tetrachloride (2.5 m)

So, P_A_bottom = 120 KPa + 1200 kg/m^3 * 9.81 m/s^2 * 2.5 m = 147.3 KPa

Step 2: Calculate the pressure at the bottom of pipe B.

The pressure at the bottom of pipe B is just the pressure at the top, since there is no column of fluid above it.

P_B_bottom = P_B_top = 200 KPa

Step 3: Find the difference in pressure.

ΔP = P_B_bottom - P_A_bottom = 200 KPa - 147.3 KPa = 52.7 KPa

So, the difference in pressure measured by the mercury in the U-tube is 52.7 KPa.

To solve this problem, we need to calculate the pressure at the same level in the U-tube for both pipes and then find the difference.

Step 1: Calculate the pressure at the bottom of pipe A.

The pressure at the bottom of pipe A is the pressure at the top plus the pressure due to the column of carbon tetrachloride.

P_A_bottom = P_A_top + ρ_CCl4 * g * h

where: P_A_top = 120 KPa ρ_CCl4 = specific gravity of CCl4 * ρ_water = 1.2 * 1000 kg/m^3 = 1200 kg/m^3 g = 9.81 m/s^2 h = 2.5 m

So, P_A_bottom = 120 KPa + 1200 kg/m^3 * 9.81 m/s^2 * 2.5 m = 147.3 KPa

Step 2: Calculate the pressure at the bottom of pipe B.

The pressure at the bottom of pipe B is just the pressure at the top of pipe B because there is no column of fluid above it.

P_B_bottom = P_B_top = 200 KPa

Step 3: Find the difference in pressure at the bottom of the two pipes.

ΔP = P_B_bottom - P_A_bottom = 200 KPa - 147.3 KPa = 52.7 KPa

Step 4: Convert this pressure difference to a height of mercury.

h_mercury = ΔP / (ρ_mercury * g)

where: ρ_mercury = 13600 kg/m^3

So, h_mercury = 52.7 KPa / (13600 kg/m^3 * 9.81 m/s^2) = 0.38 m

So, the difference in pressure measured by the mercury in the U-tube is 0.38 m of mercury.