Let's break down and solve the problem step-by-step. --- ## Problem Restatement You have a-tube manometer system: - at point 2 (open to the atmosphere) is ** psi (atmospheric pressure)**. - You need to find **the pressure at point 1** (over the bit), so the system is in equilibrium (levels are equal). - The answer is given as **7.5 psi**. --- ## Step 1: Understand the U-Tube Manometer A U-tube manometer measures pressure difference by the height difference of the fluid in the two arms. The pressure at each end of the U-tube can be written as: \[ P_1 + \rho_{fluid} g h_1 = P_2 + \rho_{fluid} g h_2 \] Where: - \(P_1\), \(P_2\) = pressure at each end (points 1 and 2) - \(\rho_{fluid}\) = density of the manometer fluid - \(h_1\), \(h_2\) = heights of fluid columns at each side For equilibrium and same fluid, the height difference is due to pressure difference. --- ## Step 2: Assign Known Values From the image and description: - \(P_2 = \) psi (atmospheric) - The fluid in the manometer is likely drilling mud or similar (details not specified, but answer provided helps) - We are to find \(P_1\) required to balance the column. --- ## Step 3: Write the Pressure Balance Equation Assume the height difference in the U-tube column is \(h\). Since the fluid is the same on both sides and the open side is at atmospheric pressure: \[ P_1 = P_2 + \rho_{fluid} g h \] But since \(P_2 = \): \[ P_1 = \rho_{fluid} g h \] --- ## Step 4: Relate Given Answer to Calculations The answer is **7.5 psi**. Let's check the units: 1 psi = 6894.76 Pa (N/m²). So: \[ 7.5\, \text{psi} = 7.5 \times 6894.76 = 51710.7 \, \text{Pa} \] If you were given a height and density, you could check this with: \[ P_1 = \rho g h \] But since the answer is given, the key point is **the pressure at point 1 must be 7.5 psi higher than atmospheric** for the column to be level (for equilibrium). --- ## Step 5: Final Answer ### **Final Answer** > The pressure required at point 1 to equilibrate the system is **7.5 psi**. --- ### **Explanation** - The U-tube manometer measures the pressure difference between point 1 (over the bit) and point 2 (atmosphere). - For equilibrium, the pressure at point 1 must exactly balance the pressure due to the column of fluid, which is equivalent to 7.5 psi. - Therefore, the required pressure at point 1 is **7.5 psi**. --- If you have more details (height or fluid density), I can show the full calculation; but this is the conceptual process and matches the answer provided.