Practice Problems on the Linear Momentum Equations
C. Wassgren, Purdue University
Page 1 of 49
Last Updated:
2010 Sep 16
COLM_01
A frequently used hydraulic brake consists of a movable ram that displaces water from a slightly larger cylinder, as
shown in the figure.
The cross-sectional area of the cylinder is
A
c
and the cross-sectional area of the ram is
A
r
.
The
ram velocity,
V
, remains constant.
Assume that the gap between the cylinder and the ram is much smaller than the
displacement of the ram
x
.
a.
Determine the water velocity as it leaves the cylinder.
b.
Determine the force
F
on the ram in terms of
A
r
,
A
c
, and
V
.
Assume that the cylinder is initially full of water,
that gravitational effects are negligible, and that the water exits the cylinder to atmospheric pressure.
Answer(s):
1
out
1
c
r
c
r
r
V
A
A
V
A
A
A
2
3
2
2
c
r
r
c
c
r
A A
F
V
A
A
A
A
x
V
F
A
c
A
r
water filled
cylinder

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