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3-74 A 6-m-high, 5-m-wide rectangular plate blocksthe end of a 5-m-deep freshwater channel, as shown inFig. P3-74. The plate is hinged about a horizontal axis alongits od ser edge through a point A and is restrained from open-ing by a fixed ridge at point B. Determine the force exertedon the plate by the ridge.AT1 m5 mBcisDFIGURE P3-74Reconsider Prob. 3-74. Using appropriate soft-ware, investigate the effect of water depth on theforce exerted on the plate by the ridge. Let the water depthvary from 0 to 5 m in increments of 0.5 m. Tabulate and plot3-75your results.

Question
3-74 A 6-m-high, 5-m-wide rectangular plate blocks
the end of a 5-m-deep freshwater channel, as shown in
Fig. P3-74. The plate is hinged about a horizontal axis along
its od ser edge through a point A and is restrained from open-
ing by a fixed ridge at point B. Determine the force exerted
on the plate by the ridge.
A
T
1 m
5 m
B
cisD
FIGURE P3-74
Reconsider Prob. 3-74. Using appropriate soft-
ware, investigate the effect of water depth on the
force exerted on the plate by the ridge. Let the water depth
vary from 0 to 5 m in increments of 0.5 m. Tabulate and plot
3-75
your results.
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3-74 A 6-m-high, 5-m-wide rectangular plate blocks the end of a 5-m-deep freshwater channel, as shown in Fig. P3-74. The plate is hinged about a horizontal axis along its od ser edge through a point A and is restrained from open- ing by a fixed ridge at point B. Determine the force exerted on the plate by the ridge. A T 1 m 5 m B cisD FIGURE P3-74 Reconsider Prob. 3-74. Using appropriate soft- ware, investigate the effect of water depth on the force exerted on the plate by the ridge. Let the water depth vary from 0 to 5 m in increments of 0.5 m. Tabulate and plot 3-75 your results.

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check_circleAnswer
Step 1

From the given diagram water is touching the plate for 5m height and 5 meters wide i.e., the  surface area of the plate which is in contact with water is 5m*5m.

We can find the pressure force on the plate by using the following formula:

Fp p g* Ah
kg
p density of liquid 1000
m3
g acceleration due to gravity 10 m/s2
Surface area of the plate which is in contact with water =5 *5 25 m2
A
-
5
2.5 m
h
distance of centroid of the area A from the surface of water
2
Therefore
Pressure Force: Fp
10 25 2.5
625000 N
625 kN
1000
k
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Image Transcriptionclose

Fp p g* Ah kg p density of liquid 1000 m3 g acceleration due to gravity 10 m/s2 Surface area of the plate which is in contact with water =5 *5 25 m2 A - 5 2.5 m h distance of centroid of the area A from the surface of water 2 Therefore Pressure Force: Fp 10 25 2.5 625000 N 625 kN 1000 k

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Step 2

Pressure force Fp acts at centre of pressure (h*), we can find centre of pressure as follows:

IG
Centre of pressure from the free surface of water (h*) =
h
A h
Moment of inertia of area A about an axis passing through it's Centre of Gravity
IG
b*d3
IG=
5*53
52 m4 (only for that area of the plate which is submerged in water)
12
12
25 m2 and h = 2.5 m
From step 1: A
52
2.5
Centre of pressure (h*) =
3.332 meters
25 2.5
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Image Transcriptionclose

IG Centre of pressure from the free surface of water (h*) = h A h Moment of inertia of area A about an axis passing through it's Centre of Gravity IG b*d3 IG= 5*53 52 m4 (only for that area of the plate which is submerged in water) 12 12 25 m2 and h = 2.5 m From step 1: A 52 2.5 Centre of pressure (h*) = 3.332 meters 25 2.5

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Step 3

Forces acting on the plate are as ...

A
RA
1 m
h*
Fp
5 m
RB
B3
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A RA 1 m h* Fp 5 m RB B3

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