# Step-by-Step Solution Let's break down the problem: - **Altitude:** \( 10,000 \) ft - **Compressor Pressure Ratio:** \( 2.5 \) - **Standard sea level pressure:** \( P_ = 101.325 \) kPa (\(14.7\) psi) - **Find:** Output pressure of the compressor at \( 10,000 \) ft --- ## 1. Find Ambient Pressure at 10,000 ft Use the standard atmosphere tables or the barometric formula. At \( 10,000 \) ft (\(3,048\) m), the standard pressure is approximately: \[ P_{10,000\ \text{ft}} \approx 10.11\ \text{psi} = 69.7\ \text{kPa} \] Alternatively, use the simplified pressure ratio formula: \[ P = P_ \left(1 - \frac{L h}{T_}\right)^{\frac{gM}{RL}} \] Where: - \(P_ = 101.325\) kPa (sea level pressure) - \(h = 3,048\) m - \(L = .0065\) K/m (temperature lapse rate) - \(T_ = 288.15\) K (sea level temp) - \(g = 9.80665\) m/s² - \(M = .0289644\) kg/mol - \(R = 8.31447\) J/(mol·K) But for practical cases, it's fine to use the standard pressure at 10,000 ft: \[ P_{10,000\ \text{ft}} \approx 10.11\ \text{psi} \] --- ## 2. Apply Compressor Pressure Ratio The **output pressure** of the compressor is: \[ P_{\text{out}} = P_{\text{ambient}} \times \text{Pressure Ratio} \] Where: - \(P_{\text{ambient}} = 10.11\) psi - Pressure Ratio \(= 2.5\) \[ P_{\text{out}} = 10.11\ \text{psi} \times 2.5 = 25.28\ \text{psi} \] --- ## 3. Final Answer **The output pressure of the turbocharger compressor at 10,000 ft is:** \[ \boxed{25.3\ \text{psi}} \] --- ### Summary Table | Altitude | Ambient Pressure (psi) | Pressure Ratio | Compressor Output (psi) | |---------------|-----------------------|---------------|------------------------| | Sea Level | 14.7 | 2.5 | 36.8 | | 10,000 ft | 10.11 | 2.5 | 25.3 | **Note:** If you need the answer in kPa, \( 25.3\ \text{psi} \approx 174.5\ \text{kPa} \). --- ## **Key Steps Recap** 1. Find ambient pressure at altitude. 2. Multiply by compressor pressure ratio. 3. State final output pressure.