Question

ME 341-Fluid Mechanics I Fall 2018 Example Problem #16 Consider a rocket moving straight up in the gravity field, as shown in the figure below. Let the initial mass of the rocket be Mo, and assume a steady exhaust mass flow rate m and exhaust velocity (relative to the rocket). If the flow pattern within the rocket motor is steady, and aerodynamic drag is neglected, derive the differential equation of the vertical rocket motion V(t) and integrate the equation using the initial condition V = 0 at t =0. Plot your resulting expression for V(t) over a range which is consistent with the assumption that the total fuel mass is one-half of the nitial rocket mass (perhaps, since no numerical values are provided, you should create a dimensionless plot). Report an expression for the maximum velocity of the rocket for these conditions. V(t) As a challenge, consider how you would account for the drag as the rocket moves through the atmosphere. And how might you model the atmosphere? No work above this line will be evaluated except identifying a control volume