 Tap water stands in a glass tube of 0.32 in. diameterat a height of 4.50 inches. What is the true static height? Use ō = 0.00504lb/ft.

To calculate the **true static height** of water in the tube, we need to account for the correction due to **capillarity**, which depends on the diameter of the tube and surface tension forces.

Given:

- Diameter of the tube: \( d = 0.32 \, \text{in} \)
- Observed height: \( h = 4.50 \, \text{in} \)
- Surface tension coefficient (\( \sigma \)): \( \sigma = 0.00504 \, \text{lb/ft} \)

We’ll convert the dimensions to consistent units (feet), compute the capillary rise, and adjust the observed height to get the **true static height**.

### Step 1: Convert the units to feet

- Diameter of the tube:  
  \( d = 0.32 \, \text{in} \times \frac{1}{12} \, \text{ft/in} = 0.02667 \, \text{ft} \)
- Height of water:  
  \( h = 4.50 \, \text{in} \times \frac{1}{12} \, \text{ft/in} = 0.375 \, \text{ft} \)

### Step 2: Calculate the capillary rise
The capillary rise (\( h_c \)) can be approximated by:

\[
h_c = \frac{2 \sigma}{\rho g d}
\]

Where:

- \( \sigma \) is the surface tension \( (0.00504 \, \text{lb/ft}) \)
- \( \rho \) is the density of water \( (62.4 \, \text{lb/ft}^3) \)
- \( g \) is the gravitational acceleration \( (32.2 \, \text{ft/s}^2) \)
- \( d \) is the diameter of the tube \( (0.02667 \, \text{ft}) \)

Now we can calculate the capillary rise.

The capillary rise is approximately \( h_c = 0.000188 \, \text{ft} \), which is about \( 0.00226 \, \text{in} \).

### Step 3: Calculate the true static height
The **true static height** (\( h_{true} \)) can be found by subtracting the capillary rise from the observed height:

\[
h_{true} = h - h_c
\]

Where \( h = 0.375 \, \text{ft} \).

Let's calculate this.The **true static height** is approximately \( 0.3748 \, \text{ft} \), which is about \( 4.4977 \, \text{in} \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How does surface tension affect the water height in narrower tubes?
2. How would a different liquid with higher surface tension impact the result?
3. What is the effect of temperature on the surface tension and water height?
4. How can capillary action be used in practical applications?
5. What are some real-world examples of capillary rise?

**Tip:** Capillary action is more pronounced in tubes with smaller diameters, causing liquids to rise or fall more noticeably.

Tap water stands in a glass tube of 0.32 in. diameter at a height of 4.50 inches. What is the true static height? Use ō = 0.00504lb/ft.

Learn how to calculate the true static height of water in a glass tube considering capillary rise. The problem involves capillary action, surface tension (0.00504 lb/ft), and fluid mechanics concepts, with step-by-step unit conversions and calculations. Suitable for undergraduate fluid mechanics students.

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