Problem 4.156

# Problem 4.156 - Problem 4.156[Difficulty 3 Given Data on...

This preview shows pages 1–2. Sign up to view the full content.

Problem 4.156 [Difficulty: 3] Given: Data on system Find: Jet speed to stop cart after 1 s; plot speed & position; maximum x; time to return to origin Solution: Apply x momentum Assumptions: 1) All changes wrt CV 2) Incompressible flow 3) Atmospheric pressure in jet 4) Uniform flow 5) Constant jet area The given data is ρ 999 kg m 3 = M 100 kg = A 0.01 m 2 = U 0 5 m s = Then a rf M u 1 ρ VU + () A [] u 2 m 2 + u 3 m 3 + = where a rf dU dt = u 1 + = and u 2 u 3 = 0 = Hence dU dt M ρ + 2 A = or dU dt ρ + 2 A M = which leads to dV U + + 2 ρ A M dt = Integrating and using the IC U = U 0 at t = 0 UV 0 + 1 ρ A 0 + M t + + = To find the jet speed V to stop the cart after 1 s, solve the above equation for V , with U = 0 and t = 1 s. (The equation becomes a quadratic in V ). Instead we use Excel 's Goal Seek in the associated workbook From Excel V5 m s = For the position x we need to integrate dx dt U = V 0 + 1 ρ A 0 + M t + + = The result is xV t M ρ A ln 1 ρ A 0 + M t + + = This equation (or the one for U with U = 0) can be easily used to find the maximum value of x by differentiating, as well as the time for x to be zero again. Instead we use Excel 's Goal Seek and Solver in the associated workbook From Excel

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

Problem 4.156 - Problem 4.156[Difficulty 3 Given Data on...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online