HYDRAULICS DEPARTMENT
Name:_______________________________
Subject & Section:______________________ Date Performed:________________
Instructor:____________________________ Date Submitted:________________
EXPERIMENT NO. 3
HYDROSTATIC FORCE ON PLANE SURFACES
Usually, engineers are confronted with problem of determining the force
exerted by fluids acting on walls of container, such as pipes, tanks and concrete
forms. Here, forces are due to the pressure, which is being exerted outward from
the inside of the container. On other occasions, the problem maybe to determine
the pressure exerted against submerged objects such as caissons, diving bells and
balloons. Another common problem is the determination of forces acting on gates in
the walls of these containers or submerged objects. Forces acting on containers or
submerged objects are due to pressure of a gas, a liquid, or a solid. In the case of
gas, pressure usually does not vary appreciably with elevation in vertical distances
that are commonly considered. With liquids, however, the pressure will vary from
atmospheric at free surface to tremendous magnitudes at great depths, such as the
ocean. The actual absolute magnitude of the pressure depends on the atmospheric
pressure, the depth of the point being considered, and the specific weight of the
liquid involved.
OBJECTIVE
This experiment determines the hydrostatic force on a submerged and semi-submerged rectangular area.
DERIVATION
Let
hs
h
d
b
=
=
=
=
vertical height from fulcrum to water surface
vertical height from water surface to top of quadrant plane surface
height of end surface of quadrant
width of end face quadrant = 75 mm
Consider a strip across the end face of the quadrant dx at a depth x, force on that
strip = ρgxbdx.
12
(Please refer to your lecture notes)
h
x
dF
dx
x
d
b = 75 mm
From:
P = γLh
therefore P= γLx
P= F/A = dF/dA
therefore dF = PdA
dF = γLxbdx
dF  
hd
h
 L gbxdx`
Therefore, the total force on the end surface
F

gb h  d   h 2
2

-------------------------------------------- (1)
2
For partially submerged surface, h=0. Therefore,
F
gbd 2
2
13
Taking moments about the surface,
Fx  dFx
Fx  
hd
h
Fx 
gbx 2 dx

gb h  d   h 3
3
3
 ----------------------------------------------- (2)
Where x = depth of center of pressure
Dividing Equation 2 by Equation 1:

gb h  d   h 3
3

3
F

gb h  d   h 3
3
3
2
gb h  d   h 2
2
3
2
2
3
3
2h  3dh  3d h  d  h 
x
3h 2  2dh  d 2  h 2 
x

2 3h 2  3hd  d 2
x
32h  d 




---------------------------------------------- (3)
For partially submerged surface, h=0
x

2d
3
Taking moment about the fulcrum
APPARATUS
Hydrostatic Pressure Apparatus
Hydraulic Bench
14
LABORATORY PROCEDURE
Place the apparatus on the hydraulic bench. Level the apparatus using the spirit
level and adjustable feet. Ensure pump delivery valve is fully closed. Connect flexible
supply hose to apparatus. Adjust the counterweight to balance the counter balance
beam until the beam is level. Switch on the pump. Place a mass of approximately 50
grams on the pan. Open pump delivery valve and allow water into the tank until
balance arm is horizontal, then close the pump delivery valve. Read height of water
level on scale or torroid. Repeat the same procedure for various values of weight in
the balance pan up to four trials. Stop Hydraulics Bench pump. Disconnect supply
hose from the apparatus and allow apparatus to drain.
Adjustable
Screw
Knife-edge
Counter balance
point
hs
200mm
h
Weight Pan
d
Drain Plug
FIGURE 1
15
APPLICATION OF PRINCIPLE
1. Comment on the variation of thrust with depth.
2. Comment on the relationship between the depth of the center of pressure
and the depth of immersion.
3. For both 1 and 2, comment on what happens when the plane has become
fully submerged.
4. Explain and comment on the discrepancies between the experimental and the
theoretical results of the depth of center of pressure.
16
FINAL DATA SHEET
NAME:_____________________________________________________
SUBJECT & SECTION:_______________________________________
SEAT NO. __________
DATE: _______________________
GROUP NO.___________________
EXPERIMENT NO.3
HYDROSTATIC FORCE ON PLANE SURFACE
GROUP
NO.
1
2
3
4
TRIAL
NO.
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
W
(g)
h
(mm)
d
(mm)
h+d
(mm)
hs
(mm)
17
x
(mm)
x + hs
(mm)
F
(N)
F(x+ hs)
(N-mm)
Wr
(N-mm)
GROUP
NO.
5
6
TRIAL
NO.
1
2
3
4
1
2
3
4
W
(g)
h
(mm)
d
(mm)
h+d
(mm)
hs
(mm)
18
x
(mm)
x + hs
(mm)
F
(N)
F(x+ hs)
(N-mm)
Wr
(N-mm)