13_Hydraulics Practice Quiz with Answer and Solution

Refresher - HYDRAULICS Quiz 13
PROBLEM 1-3:
A triangular plate of height h = 1.2 m and base b = 2 m is submerged vertically in a water
with its top edge (base) at the liquid surface and parallel to it.

➀ Evaluate the total force acting on one side of the plate, in N.
➁ Obtain the location of the force from the center of gravity of the plate, in mm.
➂ Obtain the location of the force from the liquid surface, in mm.

Solution: w.s. 2.0 m
➀ Total force acting on one side of the plate
h C.G.
P=γ hA d
e
1.2 m
⎛ 1.2 ⎞ ⎡ (2)(1.2) ⎤
P = 9810 ⎜ ⎟ ⎢ ⎥
⎝ 3 ⎠⎣ 2 ⎦
P = 4708.8 N

➁ Location of the force from the center of gravity of the plate
I
e= g
Ay
2.0(1.2)3
Ig = = 0.096
36
0.096
e=
2(1.2) ⎛ 1.2 ⎞
(0.9) ⎜ ⎟
2 ⎝ 3⎠
e = 0.20 m
e = 200 mm

➂ Location of the force from the liquid surface
d= h +e
1.2
d= + 0.20
3
d = 0.6 m
d = 600 mm

, Refresher - HYDRAULICS Quiz 13
PROBLEM 4:
A cubic meter of water is subjected to a pressure increase of 20 MPa. If the bulk
modulus of elasticity of the water is 2200 MPa, evaluate the change in volume in
m3 .


Solution:
− ∆P
E=
∆V
V
−(20 - 0)
2200 =
∆V
1
∆V = - 0.00909