Length of pumping chamber is 30mm. Gear Diameter is 20mm. Gear width is 16mm. 1 lite is equivalent to 1000000 mm cube. Round off final answer to four decimal places

To calculate the volume of a gear pump's chamber, we'll use the given dimensions and the formula for the volume of a cylinder, as the gear pump chamber can be approximated as a cylindrical space.

### Step 1: Calculate the Volume of the Pumping Chamber

The volume of the pumping chamber is given by:

\[
\text{Volume} = \text{Area of Gear Face} \times \text{Length of Chamber}
\]

Where the area of the gear face is the area of the circle formed by the gear's diameter.

\[
\text{Area of Gear Face} = \pi \times \left(\frac{\text{Gear Diameter}}{2}\right)^2
\]

Substituting the values:

\[
\text{Area of Gear Face} = \pi \times \left(\frac{20\text{ mm}}{2}\right)^2 = \pi \times 10^2 \text{ mm}^2 = 100\pi \text{ mm}^2
\]

Now, multiply the area by the gear width to find the volume of the chamber:

\[
\text{Volume} = 100\pi \times 16 \text{ mm}^3 = 1600\pi \text{ mm}^3
\]

### Step 2: Convert to Liters

We are given that \(1\) liter = \(1,000,000\) mm³. To convert the volume from mm³ to liters:

\[
\text{Volume in Liters} = \frac{1600\pi \text{ mm}^3}{1,000,000 \text{ mm}^3/\text{liter}} = \frac{1600\pi}{1,000,000} \text{ liters} = \frac{1600 \times 3.1416}{1,000,000} \text{ liters}
\]

### Step 3: Calculate the Final Volume

\[
\text{Volume in Liters} = \frac{5026.56}{1,000,000} \text{ liters} = 0.00502656 \text{ liters}
\]

### Step 4: Round to Four Decimal Places

The final volume rounded to four decimal places is:

\[
\text{Volume} \approx 0.0050 \text{ liters}
\]

### Final Answer:
The volume of the pumping chamber is approximately **0.0050 liters**.

Would you like any further clarifications or have additional questions?

### Further Questions:
1. How does the gear width affect the volume of the pumping chamber?
2. What would happen to the chamber volume if the gear diameter was increased by 10%?
3. How do you calculate the flow rate of the gear pump if the RPM is known?
4. How does the length of the chamber impact the overall performance of the pump?
5. What is the relationship between the chamber volume and the pump efficiency?

### Tip:
Always ensure unit consistency when performing volume calculations, especially when converting between different units of measurement.

Learn how to calculate the volume of a gear pump's chamber using geometry and unit conversion. This problem involves calculating the volume of a cylinder, converting mm³ to liters, and rounding to four decimal places. Suitable for high school students studying geometry and unit conversions.

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