Difficulty: Easy
Correct Answer: F = (w / g) * a * V^2
Explanation:
Introduction:
The impact force of a jet on surfaces follows directly from Newton's second law applied to a control volume. Using specific weight instead of density is common in hydraulic machinery problems, necessitating careful unit conversions.
Given Data / Assumptions:
Concept / Approach:
Force equals rate of change of momentum. For normal impact on a fixed plate, the outgoing normal velocity is approximately zero, so the momentum reduction equals rho * a * V * V. Express density as rho = w / g to obtain the force in terms of w.
Step-by-Step Solution:
Mass flow rate: m_dot = rho * a * V = (w / g) * a * V.Momentum change per second: m_dot * V = (w / g) * a * V^2.Hence, force on plate: F = (w / g) * a * V^2.
Verification / Alternative check:
Dimensional check: w/g has units of kg/m^3; multiplied by a * V^2 yields N.
Why Other Options Are Wrong:
w * a * V: missing one factor of V and g; incorrect units.(w * a * V^2) / (2 * g): the 1/2 factor applies to energy, not momentum force in this case.(w * V) / a: dimensionally inconsistent.
Common Pitfalls:
Mixing energy head expressions (V^2 / 2g) with momentum-based force calculations.
Final Answer:
F = (w / g) * a * V^2
Discussion & Comments