Do the work for this problem clearly on scratch paper. 3 You MUST show this work in the photo/pdf on the final question on this quiz. (See the last question for details) 6 The answer here will count for only 2 marks. Your correct work in the photo will count for an additional 2 marks. Fan Affinity Problem: A pump system has is rated at POWERold \( =900 \) Watts \( (\mathrm{W}) \) and has an RPMold \( = \) 600. If the power is increased to POWERnew \( =1800 \mathrm{~W} \), what will the new shaft speed RPMnew be? Fan affinity law for power and shaft speed. \[ \frac{P O W E R_{\text {old }}}{P O W E R_{\text {new }}}=\frac{\left(R P M_{\text {old }}\right)^{3}}{\left(R P M_{\text {new }}\right)^{3}} \] State your answer to the nearest whole number. Do not worry about units in this question. Your Answer: Answer

Sure, let's solve the problem step by step using the fan affinity laws. **Given:** - **POWER_old (\( P_{\text{old}} \))** = 900 Watts - **RPM_old (\( \text{RPM}_{\text{old}} \))** = 600 - **POWER_new (\( P_{\text{new}} \))** = 1800 Watts **Objective:** Find the new shaft speed (\( \text{RPM}_{\text{new}} \)) when the power is increased to 1800 Watts. **Fan Affinity Law:** The relationship between power and rotational speed is given by: \[ \frac{P_{\text{old}}}{P_{\text{new}}} = \left( \frac{\text{RPM}_{\text{old}}}{\text{RPM}_{\text{new}}} \right)^3 \] **Steps:** 1. **Set up the equation:** \[ \frac{900}{1800} = \left( \frac{600}{\text{RPM}_{\text{new}}} \right)^3 \] 2. **Simplify the ratio:** \[ \frac{1}{2} = \left( \frac{600}{\text{RPM}_{\text{new}}} \right)^3 \] 3. **Take the cube root of both sides to solve for \( \frac{600}{\text{RPM}_{\text{new}}} \):** \[ \left( \frac{1}{2} \right)^{1/3} = \frac{600}{\text{RPM}_{\text{new}}} \] \[ 2^{-1/3} = \frac{600}{\text{RPM}_{\text{new}}} \] \[ \text{RPM}_{\text{new}} = 600 \times 2^{1/3} \] 4. **Calculate \( 2^{1/3} \) (approximately 1.26):** \[ \text{RPM}_{\text{new}} = 600 \times 1.26 = 756 \] **Final Answer:** \[ \text{RPM}_{\text{new}} = 756 \text{ (rounded to the nearest whole number)} \]