A4-ft tall, 8-in wide concrete (150lb/ft3)

retainingwall is built. during a heavy rain, water fills the

spacebetween the wall and the earth behind it to a depth, h.

determine the maximum depth of water possible without the

walltipping over. the wall simply rests on the ground withoutbeing

anchored to it.

maximum possible height of water is 2.34 ft without wall tipping

Explanation:

given data

wall height = 4 ft

wall width = 8 in = 0.667 ft

weight density = 150 lb/ft³

to find out

the maximum depth of water possible without the  wall tipping

solution

we find here first weight of concrete wall that is

weight = volume × weight density

weight = length × width × height × weight density

weight = 150 × 4 × 0.667 × L

weight = 400 L lb

here L is length

now find the resulting force acting due to hydrostatic force per unit length

Fr = density of water × hc × ( h×L)

heer hc is distance between fluid surface and centroid area = and L is length and h is height

and density of water is 62.4 lb/ft³

so Fr = 62.4 × × ( h×L)

Fr = 31.2 h²L

now

point of position of apply resultant force that is Yr

Yr =

Yr =

Yr =

so

moment about about point A will be  zero to avoid tapping

so

∑Ma = 0

h = 2.34

so maximum possible height of water is 2.34 ft without wall tipping

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explanation: