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
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To solve the Fan Affinity Problem using the provided formula, we first rearrange it to solve for the new RPM. Start with the equation: \[ \frac{POWER_{old}}{POWER_{new}} = \frac{(RPM_{old})^3}{(RPM_{new})^3} \] Plugging in the values: \[ \frac{900}{1800} = \frac{(600)^3}{(RPM_{new})^3} \] This simplifies to: \[ \frac{1}{2} = \frac{(600)^3}{(RPM_{new})^3} \] To find \( RPM_{new} \), cross-multiply and rearrange: \[ RPM_{new}^3 = 2 \times (600)^3 \] Calculating \( (600)^3 = 216000000 \): \[ RPM_{new}^3 = 2 \times 216000000 = 432000000 \] Now, taking the cube root: \[ RPM_{new} = \sqrt[3]{432000000} \approx 750 \] Thus, the new shaft speed is approximately **750** RPM. Your Answer: 750
