Mechanical Engineering Problems and Solutions

Unit name:
Title of experiment:
Date:
Student ID:
Student name:

Problem1: A viscous damper consists of a piston in a cylinder containing oil of viscosity
0.38 Ns/m as a damping fluid. the length of the piston is 100 mm and it has a four 6mm
holes between its faces. If the damping constant is required to be 26 kN.s/m, find the piston
diameter.
Solution 1: Here the problem is depending on the diameter of piston can be roughly
represented as
e= MA
t
C=26 kN.s/m
Area provide fluid friction
¿ 2 πr ×100+ 4 × 2 π ×3 ×100
¿ 200 π ( r+ 12 ) mm2

Here t=3 mm
So,
26 ×1000= 0.38(200 π ( r +12 ))
3 ×1000
200 π ( r+ 12 ) = 78000000
0.38
( r +12 ) =326686.46
r =326674.46 m
Diameter of piston is 6.5 x 105 m
Problem 2: A model was designed to simulate the response of a human head to a frontal
blow. the model has a mass of 4.7 kg horizontally supported by a spring of stiffness 2000
N/m. If a blow of 400 N was applied to the mass over a period of 0.003 seconds. Find the
maximum acceleration which the mass is subjected to as a result of this blow. What’s the
maximum deflection in the spring.
Solution 2:
We know
F.t= change in momentum
Ft=mV f −mV i