Let's solve the problem **step by step**: # **Step 1: Understand the Coriolis Flow Meter Principle** The mass flow rate, \( \dot{m} \), in a Coriolis flow meter is related to the twist angle (\(\delta\)) by the equation: \[ \dot{m} = \frac{K_s \cdot \delta}{2 \omega L r} \] Where: - \(K_s\) = Angular spring constant (N·m/degree) - \(\delta\) = Twist angle (degree) - \(\omega\) = Angular velocity (rad/s) - \(L\) = Tube length perpendicular to vibrating axis (m) - \(r\) = Radius of curved portion of tube (m) --- # **Step 2: Convert Units if Necessary** - \(\delta = 0.5^\circ\) needs to be converted to **radians**: \[ 1^\circ = \frac{\pi}{180} \text{ radians} \] \[ \delta = 0.5 \times \frac{\pi}{180} = 0.00873 \text{ radians} \] - \(K_s = 16,500\) N·m/degree Convert to N·m/radian: \[ K_s (\text{N·m/rad}) = 16,500 \times \frac{180}{\pi} = 945,000 \text{ N·m/rad} \] --- # **Step 3: Plug in the Values** Given: - \(K_s = 945,000\) N·m/rad - \(\delta = 0.00873\) radians - \(\omega = 600\) rad/s - \(L = 0.47\) m - \(r = 0.28\) m \[ \dot{m} = \frac{945,000 \times 0.00873}{2 \times 600 \times 0.47 \times 0.28} \] --- # **Step 4: Calculate the Numerator and Denominator** **Numerator:** \[ 945,000 \times 0.00873 = 8,248.85 \] **Denominator:** \[ 2 \times 600 \times 0.47 \times 0.28 = 2 \times 600 = 1200 \\ 1200 \times 0.47 = 564 \\ 564 \times 0.28 = 157.92 \] --- # **Step 5: Calculate the Mass Flow Rate (kg/s)** \[ \dot{m} = \frac{8,248.85}{157.92} = 52.25 \text{ kg/s} \] --- # **Step 6: Convert to kg/hour** \[ 1 \text{ hour} = 3600 \text{ seconds} \] \[ \dot{m}_{\text{hour}} = 52.25 \times 3600 = 188,100 \text{ kg/hour} \] --- # **Final Answer** \[ \boxed{188,100 \text{ kg/hour}} \] --- ## **Summary Table** | Step | Value | |---------------|--------------| | \(K_s\) (N·m/rad) | 945,000 | | \(\delta\) (rad) | 0.00873 | | Numerator | 8,248.85 | | Denominator | 157.92 | | Mass flow (kg/s) | 52.25 | | Mass flow (kg/hour) | 188,100 | --- Let me know if you have any questions about the calculation!