Oil Tanker and Road Surface Calculations Assignment

Oil Tanker and Road Surface Calculations Assignment

Description of Assessment Task and Purpose:

Question 1

  1. Consider the oil tank below that has a constant cross-sectional with a diameter of 1m. The tank is designed to feed the turbocharger of a large diesel engine in the case of a power black-out. The tank must provide oil to the turbocharger to prevent damage during its emergency shut-down which takes approximately 10 seconds. In order to maintain oil pressure to the turbocharger the oil must not drop below a height of 10cm during these 10 seconds.
  1. Form a differential equation that represents the system. (5 marks)
  1. Solve the differential equation given that h=h0 att=0. (10 marks)

(c) Determine the time it will take for the tank to reach the minimum level of 10cm if the initial height of oil, h0, is 50cm and k=0.05 , plot a graph of h against t and hence decide if the tank is suitable. (5 marks)

Question 2

A car suspension system consisting of a spring and viscous damper carries a mass of 250kg. The damping coefficient, c, of the damper is 110Ns/m and the spring stiffness, k, is 600 N/m. The road surface subjects the system to a sinusoidal force of 10N at an angular frequency of 2 rad/s.

  1. Form a differential equation that represents the system. (5 marks)

(b) Solve the homogeneous equation and plot a graph of xagainst tin order to show the transient response of the system if the initial displacement, x0 =0.03 m and dx/dt=0 at t=0. (10 marks)

(c) Solve the non-homogeneous equation and plot graphs of xagainst tin order to show the steady-state and overall response of the system. (10 marks)

(d) Describe the overall response of the suspension system making reference to your solution. (5 marks)

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