Q1: For the manometer set up shown in the figure, the pressure difference P_A - P_B is given by

ANS:A - (ρH - ρ_air)gH

It seems like you intended to describe a figure or diagram related to a manometer setup, but unfortunately, I cannot view or interpret images. However, I can help explain how to determine the pressure difference PA−PBP_A - P_BPA​−PB​ in a typical manometer setup based on common configurations.

Manometer Basics:

A manometer is a device used to measure pressure differences between two points in a fluid by balancing the weight of the fluid between the two points. Here’s how you can determine PA−PBP_A - P_BPA​−PB​ based on the setup:

1. Types of Manometers:
   • Open-end Manometer: One end is open to the atmosphere.
   • Closed-end (Differential) Manometer: Both ends are connected to different points in a system.
2. Calculation Method:
   • For an open-end manometer, the pressure difference PA−PBP_A - P_BPA​−PB​ is determined by the difference in the heights of the fluid columns in the two arms of the manometer. The pressure difference is given by: PA−PB=ρ⋅g⋅(hB−hA)P_A - P_B = \rho \cdot g \cdot (h_B - h_A)PA​−PB​=ρ⋅g⋅(hB​−hA​) where:
     • ρ\rhoρ is the density of the manometric fluid (typically mercury or water),
     • ggg is the acceleration due to gravity,
     • hAh_AhA​ and hBh_BhB​ are the heights of the fluid columns on the respective sides of the manometer.
   • For a closed-end (differential) manometer, the pressure difference PA−PBP_A - P_BPA​−PB​ is given by: PA−PB=ρ⋅g⋅(hA−hB)P_A - P_B = \rho \cdot g \cdot (h_A - h_B)PA​−PB​=ρ⋅g⋅(hA​−hB​) Here, hAh_AhA​ and hBh_BhB​ represent the heights of the fluid columns on the two sides of the manometer, typically relative to the same reference level.
3. Determining Pressure Difference:
   • Identify which side (A or B) is connected to the higher pressure source.
   • Measure the difference in height between the two fluid columns hAh_AhA​ and hBh_BhB​.
   • Use the formula appropriate for your manometer setup (open-end or closed-end) to calculate PA−PBP_A - P_BPA​−PB​.

Conclusion:

To provide a precise calculation for PA−PBP_A - P_BPA​−PB​, the specific details of the manometer setup, such as whether it's open-end or closed-end and the fluid used, are crucial. If you can describe the setup or provide additional details, I can help further with the calculation.