A vertical plate is partially submerged in water and has the indicated shape. The height is 3m, the width at the top is 4m, and
the width at the bottom is 8m. Label the shape (trapezoid) appropriately. Express the hydrostatic force against one side of the plate as an integral and evaluate it, if the water level is 1 m from the top of the plate.
1 answer:
Answer: 1.98 × 10^4 N
Explanation:
Form similar triangle ADE and ABC
a/x= 2/3, a=2/3x
Width of the strip w= 2(4+a) = 8+2a
W= 8 +2 (2/3x)= 8+4/3x
Area of the strip = w Δx
(8 +4/3x) Δx
Pressure on the strip p= pgx= 10^3 ×9.81x= 9810x
But,
Force= Pressure × area= 9810x × (8+4/3x)Δx
Adding the forces and taking lim n to infinity
F total= lim n--> infinity E 9810x × (8+4/3x)Δx
Ftotal= Integral 2,0 9810x × (8+4/3x)Δx
F total= 9810 integral 2, 0 (8+4/3x)dx
= 9810(8+x^2/2 + 4/3x^3/3)2,0
=9810(4x^2 + 4/9x^3)
=9810(4x2^2 + 4/9×2^3-0)
=9810(16 + 32/9)
Hydrostatic force as an integral
Ft= 19.18 ×10^4N
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Answer:
a) 35%
b) yes it can be improved by moving the tray near the top
Tray should be located ( 1 to 2 meters below surface )
max removal efficiency ≈ 70%
c) The maximum removal will drop as the particle settling velocity = 0.5 m/h
Explanation:
Given data:
flow rate = 8000 m^3/d
Detention time = 1h
depth = 3m
Full length movable horizontal tray : 1m below surface
<u>a) Determine percent removal of particles having a settling velocity of 1m/h</u>
velocity of critical sized particle to be removed = Depth / Detention time
= 3 / 1 = 3m/h
The percent removal of particles having a settling velocity of 1m/h ≈ 35%
<u>b) Determine if the removal efficiency of the clarifier can be improved by moving the tray, the location of the tray and the maximum removal efficiency</u>
The tray should be located near the top of the tray ( i.e. 1 to 2 meters below surface ) because here the removal efficiency above the tray will be 100% but since the tank is quite small hence the
Total Maximum removal efficiency
= percent removal + percent removal
= ( d,v
) .
+ ( d
,v
) .
= 100
hence max removal efficiency ≈ 70%
<u>c) what is the effect of moving the tray would be if the particle settling velocity were equal to 0.5m/h?</u>
The maximum removal will drop as the particle settling velocity = 0.5 m/h
