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
Here's how to solve the problem: a) The total force required on the piston. Step 1: Convert the given values to SI units. • Pressure, P = 800 kPa = 800 × 10^3 Pa • Plunger diameter, D = 220 mm = 0.220 m Step 2: Calculate the cross-sectional area of one piston. The area (A) of a circular piston is given by the formula A = ( D^2)/(4). A = (0.220 m)^24 A = × 0.0484 m^24 A = 0.0121 m^2 A ≈ 0.038013 m^2 Step 3: Calculate the force required on one piston. The force (F) is calculated using the formula F = P × A. F = (800 × 10^3 Pa) × (0.038013 m^2) F = 30410.4 N The total force required on one piston is 30410.4 N. b) The work done during 10 delivery strokes. Step 1: Convert the stroke length to SI units. • Stroke length, L = 380 mm = 0.380 m Step 2: Calculate the work done by one piston during one delivery stroke. Work done (W) is calculated using the formula W = F × L. W_one\_stroke = (30410.4 N) × (0.380 m) W_one\_stroke = 11555.952 J Step 3: Calculate the total work done by the three-piston pump during 10 delivery strokes. Since there are three pistons and 10 delivery strokes, the total work done is: W_total = W_one\_stroke × number of pistons × number of strokes W_total = 11555.952 J × 3 × 10 W_total = 346678.56 J The work done during 10 delivery strokes is 346678.56 J. Drop the next question!