This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Convert the given values to SI units. The diameter D is 90 mm, which is 0.090 m. The flow rate Q is 30 L/s, which is 30 × 10^-3 m^3/s. The pressure drop P is 60 kPa, which is 60 × 10^3 Pa. The length of the pipeline L is 20 m. The density of water is approximately 1000 kg/m^3. The acceleration due to gravity g is approximately 9.81 m/s^2. Step 2: Calculate the cross-sectional area of the pipe. The area A of a circular pipe is given by A = ( D^2)/(4). A = (0.090 m)^24 = × 0.0081 m^24 ≈ 0.0063617 m^2 Step 3: Calculate the velocity of water in the pipe. The velocity V is given by V = (Q)/(A). V = 30 × 10^-3 m^3/s0.0063617 m^2 ≈ 4.7157 m/s Step 4: Calculate the head loss due to friction. The head loss h_f is related to the pressure drop P by h_f = ( P)/( g). h_f = 60 × 10^3 Pa1000 kg/m^3 × 9.81 m/s^2 = 60000 Pa9810 N/m^3 ≈ 6.1162 m Step 5: Calculate the coefficient of friction f using the Darcy formula. The Darcy-Weisbach formula for head loss is h_f = f (L)/(D) (V^2)/(2g). Rearranging to solve for f: f = (h_f · 2gD)/(L V^2) Substitute the calculated values: f = 6.1162 m × 2 × 9.81 m/s^2 × 0.090 m20 m × (4.7157 m/s)^2 f = (10.809)/(444.758) ≈ 0.0243 The value of the coefficient of friction is 0.0243. Send me the next one 📸