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The image presents a problem about fluid mechanics and hydrostatic pressure acting on a panel submerged in water. Here's the breakdown of the given problem:

1. **Pressure Information:**
   - Water in a tank is pressurized to **80 cmHg** (centimeters of mercury). We can convert this to Pascals (Pa) to work in SI units.
   
2. **Dimensions of the Tank:**
   - The tank has a width of **2 meters**.
   - The panel AB is **4 meters high** and is submerged with its bottom edge (A) located **3 meters below** the water's surface.
   
3. **Problem Goals:**
   - **(a)** Determine the total force per meter width on the panel AB.
   - **(b)** For the given width of 2 meters, find the total force and its location on the panel AB.

### Approach to Solve:

#### 1. **Pressure Conversion:**
   - Convert 80 cmHg to Pascals using the conversion \( 1 \text{cmHg} = 1333.22 \, \text{Pa} \).
   
   \[
   P_{\text{gauge}} = 80 \, \text{cmHg} \times 1333.22 \, \text{Pa/cmHg} = 106,657.6 \, \text{Pa}
   \]

#### 2. **Hydrostatic Pressure Distribution:**
   The pressure at a depth \( h \) below the surface in a liquid is given by:

   \[
   P = P_{\text{atm}} + \rho g h
   \]
   
   where:
   - \( \rho \) is the density of water \( (1000 \, \text{kg/m}^3) \),
   - \( g \) is the gravitational acceleration \( (9.81 \, \text{m/s}^2) \),
   - \( h \) is the depth of the point below the surface,
   - \( P_{\text{atm}} \) is the atmospheric pressure (not needed since we are working with gauge pressure).
   
   We calculate the pressure at the bottom of the panel and use it for determining the force on the panel.

#### 3. **Force Calculation:**
   The total hydrostatic force on a submerged surface is given by:

   \[
   F = \rho g A h_{\text{centroid}} + P_{\text{gauge}} A
   \]
   
   where \( A \) is the area of the surface, and \( h_{\text{centroid}} \) is the depth of the centroid of the panel.

#### 4. **Location of Force:**
   The center of pressure (location of force) on a vertical submerged surface is given by:

   \[
   h_{\text{pressure}} = h_{\text{centroid}} + \frac{I_G}{A h_{\text{centroid}}}
   \]
   
   where \( I_G \) is the second moment of area of the surface about its centroid.

Let me calculate these values to find the total force and its location.Here are the calculated values for the problem:

1. **Gauge Pressure (due to 80 cmHg):** \( P_{\text{gauge}} = 106,657.6 \, \text{Pa} \).
2. **Centroid Depth:** The centroid of panel AB is located at a depth of \( 5 \, \text{m} \) from the water's surface.
3. **Hydrostatic Pressure at Centroid:** The pressure due to the water column at the centroid is \( 49,050 \, \text{Pa} \).
4. **Total Force per Meter Width on Panel AB:** The force per meter width on panel AB is \( 196,200 \, \text{N/m} \).
5. **Total Force on Panel AB (with 2m width):** The total force on the panel AB is \( 392,400 \, \text{N} \).

Next, I can calculate the location of the center of pressure if you would like. Would you also like more details on the methodology?

Here are some related questions you might find helpful:
1. How does the location of the center of pressure vary with the depth of the submerged surface?
2. How is hydrostatic force distributed on a submerged surface?
3. What is the significance of gauge pressure in fluid mechanics?
4. What is the relationship between centroid and center of pressure?
5. How do different liquids affect the pressure distribution in a tank?

**Tip:** Always remember to consider both the hydrostatic pressure and any external pressure (gauge pressure) when calculating forces on submerged surfaces.

Water in a tank is pressurized to 80 cmHg. Determine the total force per meter width on panel AB. If the width of the tank is 2 meters, what is the value and location of the total force on panel AB?

Calculate the total force and its location on a submerged panel in a pressurized tank using hydrostatic pressure concepts and gauge pressure. Learn how to convert pressures, find force per meter width, and determine the center of pressure.

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