1. **Stating the problem:** Given the Reynolds number $Re = 8.8 \times 10^{4}$, find the frictional factor $f$. 2. **Formula and explanation:** For turbulent flow in smooth pipes, the friction factor $f$ can be estimated using the Blasius empirical correlation: $$f = 0.3164 \times Re^{-0.25}$$ This formula is valid for Reynolds numbers in the range $4000 < Re < 10^{5}$. 3. **Calculation:** Substitute $Re = 8.8 \times 10^{4}$ into the formula: $$f = 0.3164 \times (8.8 \times 10^{4})^{-0.25}$$ 4. **Simplify the exponent:** Calculate $Re^{-0.25} = (8.8 \times 10^{4})^{-0.25}$. First, find $Re^{0.25} = (8.8 \times 10^{4})^{0.25}$. Using properties of exponents: $$Re^{0.25} = 8.8^{0.25} \times (10^{4})^{0.25} = 8.8^{0.25} \times 10^{1}$$ Calculate $8.8^{0.25}$ (the fourth root of 8.8): approximately $1.73$. So, $$Re^{0.25} \approx 1.73 \times 10 = 17.3$$ Therefore, $$Re^{-0.25} = \frac{1}{17.3} \approx 0.0578$$ 5. **Calculate friction factor:** $$f = 0.3164 \times 0.0578 \approx 0.0183$$ 6. **Final answer:** The frictional factor $f$ is approximately **0.0183**.