Calculate the actuator forward speed in meters per second

To calculate the forward speed of the actuator in meters per second, we'll use the following steps.

### **Given Data:**
- Radius of the actuator face: \( r = 50 \, \text{mm} \)
- Flow rate: \( Q = 0.5 \, \text{litres/second} \)

### **Formulas:**
1. **Area of the Actuator Face:**
   \[
   A_{\text{face}} = \pi r^2
   \]
2. **Convert Flow Rate to Cubic Meters per Second:**
   \[
   Q = 0.5 \, \text{litres/second} = 0.5 \times 10^{-3} \, \text{m}^3/\text{s} = 0.0005 \, \text{m}^3/\text{s}
   \]
3. **Forward Stroke Speed:**
   \[
   v_{\text{forward}} = \frac{Q}{A_{\text{face}}}
   \]

### **Step-by-Step Calculation:**

1. **Calculate the Area of the Actuator Face:**
   \[
   A_{\text{face}} = \pi r^2 = \pi \times (50 \, \text{mm})^2 = \pi \times 2500 \, \text{mm}^2
   \]
   Convert to square meters:
   \[
   A_{\text{face}} = \pi \times 2500 \times 10^{-6} \, \text{m}^2 = 0.007854 \, \text{m}^2
   \]

2. **Calculate the Forward Stroke Speed:**
   \[
   v_{\text{forward}} = \frac{Q}{A_{\text{face}}} = \frac{0.0005 \, \text{m}^3/\text{s}}{0.007854 \, \text{m}^2} = 0.06367 \, \text{m/s}
   \]

### **Final Answer:**
- **Forward Stroke Speed:** \( v_{\text{forward}} \approx 0.0637 \, \text{m/s} \)

This is the speed of the actuator during the forward stroke, rounded to four decimal places as requested.

Would you like any further clarification or have additional questions?

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### **Related Questions:**
1. What would be the forward stroke speed if the radius of the actuator face were 60 mm?
2. How does increasing the flow rate affect the forward stroke speed?
3. How would changing the radius of the actuator rod affect the return stroke speed?
4. What happens to the speed if the air pressure in the system is doubled?
5. Can you explain the relationship between actuator area and speed in different flow conditions?

### **Tip:**
Always ensure that the radius and flow rate are in consistent units (e.g., meters and cubic meters) before performing calculations.

Learn how to calculate the forward speed of an actuator in meters per second using fluid mechanics principles. This problem involves determining the speed based on the radius of the actuator face and the flow rate. Suitable for advanced high school students and engineering enthusiasts.

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