Let's solve the problem step by step: --- ## **Step 1: Understand the Problem** - **Given:** - Symmetric and cambered airfoils tested at 6° angle of attack, 15 m/s wind tunnel. - Lift coefficients at critical Mach numbers: - Symmetric: \( c_{l, \text{crit}} = 1.5 \) - Cambered: \( c_{l, \text{crit}} = 1.7 \) - **Question:** What is the ratio of the surface pressure coefficients (\( C_p \)) of the symmetric airfoil to the cambered airfoil if tested in **water**? --- ## **Step 2: Relevant Formulas** ### **Lift Coefficient** \[ c_L = \frac{L}{\frac{1}{2} \rho V^2 S} \] ### **Pressure Coefficient** \[ C_p = \frac{p - p_\infty}{\frac{1}{2} \rho V^2} \] ### **Relationship** Lift is generated by the pressure difference over the airfoil, which is related to the surface pressure coefficients. For similar shapes and flow regimes, the ratio of \( c_L \) in different fluids depends on the ratio of dynamic pressures, which is related to density. --- ## **Step 3: What Changes in Water?** When moving from air to water: - The **velocity** and **angle of attack** are unchanged. - The **density** of the fluid changes significantly. **Air density (\( \rho_{air} \))**: ~1.225 kg/m³ **Water density (\( \rho_{water} \))**: ~1000 kg/m³ --- ## **Step 4: Surface Pressure Coefficient Ratio** The pressure coefficient distribution over the surface gives rise to the lift coefficient. For geometrically similar flows (same \( \alpha \), \( V \)), the ratio of pressure coefficients will be proportional to the ratio of lift coefficients (since dynamic pressure is accounted for in both). \[ \left( \frac{C_{p,\text{sym}}}{C_{p,\text{cambered}}} \right)_{water} = \frac{c_{l,\text{sym}}}{c_{l,\text{cambered}}} \] Given: - \( c_{l,\text{sym}} = 1.5 \) - \( c_{l,\text{cambered}} = 1.7 \) --- ## **Step 5: Calculate the Ratio** \[ \text{Ratio} = \frac{c_{l,\text{sym}}}{c_{l,\text{cambered}}} = \frac{1.5}{1.7} \] \[ \boxed{0.88} \] --- ## **Step 6: Final Answer** ### **The ratio of the surface pressure coefficients of the symmetric airfoil to the cambered airfoil, if tested in water, is:** \[ \boxed{0.88} \] --- ### **Summary Table** | Airfoil Type | Lift Coefficient (\(c_l\)) | Pressure Coefficient Ratio (\(C_p\)) | |-------------------|---------------------------|--------------------------------------| | Symmetric | 1.5 | 0.88 | | Cambered | 1.7 | 1 | --- **If you have any doubts or want to see the effect of density or velocity, let me know!**