Calculating the work done

• We place the fluid element in a coordinate system.
• Forces are exerted on the system by the surrounding fluid
• Force along the motion, \( F_1 = P_1 A_1 \)
• Force against the motion, \( F_2 = P_2 A_2 \)
• Since \(F_1 > F_2 \), the fluid element moves.
• Work done on the system, \( W_1 = P_1 A_1 ds_1 \)
• Work done by the system,\( W_2 = P_2 A_2 ds_2 \)