Infinite and finite length of blanket A natural impervious blanket of large areal extent if available may be considered as a balnket of infinite length For a blanket of infinite length, the solution of equation (iv) is In this case for the convenience, the point x = 0 is taken at the downstream end of the blanket and hence h0 is the total loss of head through the blanket upto the end of the blanket. As a measure of the efficiency of a blanket of any length x (where x may be infinite or a finite length) a length Xr is considered which is known as equivalent resistance of the foundation and is defined below. It may be defined as the length of a prism of the foundation soil of thickness Zf and coefficient of permeability kf which under the loss of head h would carry flow equivalent to the flow which passes the blanket system under the same loss of head. Thus (2) Solution for finite length of blanket : For a blanket of uniform thickness and finite length of blanket ihe solution equation (iv) is which h is the loss of head through the blanket upto any point at a distance and hn is a constant for computing h. hn depends on the total head loss of the system of which the blanket is a part and on the ratio of the blanket to the remainder of system. * From equation (viii) at x - 0, h = 0, and hence in this case the point x = 0 is taken at the upstream end of the blanket. Differentiating both sides of equation (viii) with respect to x, we get

1. Infinite and finite
length of blanket
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2. (a) Infinite length of blanket :
A natural impervious blanket of
large areal extent if available may
be considered as a balnket of
infinite length
For a blanket of infinite length, the
solution of equation (iv) is
v
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3. where,
h = loss of -head through the blanket
up to any point at a distance x.
h0 = loss of head through the blanket
up to a point x = 0.
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5. In this case for the convenience, the
point x = 0 is taken at the downstream
end of the blanket and hence h0 is the
total loss of head through the blanket
upto the end of the blanket.
As a measure of the efficiency of a
blanket of any length x (where x may
be infinite or a finite length) a length
Xr is considered which is known as
equivalent resistance of the
foundation and is defined below.
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6. equivalent resistance Xr of
the foundation :
It may be defined as the length of a
prism of the foundation soil of
thickness Zf and coefficient of
permeability kf which under the
loss of head h would carry flow
vi
equivalent to the flow which passes
the blanket system under the same
loss of head. Thus
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7. Also from equation (v), we have
vii
Equating the values of
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8. (2) Solution for finite length
of blanket :
For a blanket of uniform thickness and finite
length of blanket ihe solution equation (iv) is
viii
which h is the loss of head through the blanket
upto any point at a distance and hn is a
constant for computing h. hn depends on the
total head loss of the system of which the
blanket is a part and on the ratio of the
blanket to the remainder of system. *
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9. From equation (viii) at x - 0, h = 0,
and hence in this case the point x =
0 is taken at the upstream end of the
blanket.
Differentiating both sides of
equation (viii) with respect to x, we
get
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10. Again if Xr is the equivalent
resistance of the foundation, we
have from equation
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11. If the length of the blanket is L then
by substituting x = L in equation
(ix) the value of Xr for the entire
blanket is obtained.
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12. Loss of head through the
blanket :
h0 is the loss of head upto the end of
the blanket; H is the total reservoir
head Xd is the base width of the
impervious core
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13. reduction in quantity of seepage
due to provision of blanket :
When no blanket
With blanket
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19. The value of constant 'a' is
given by
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20. The optimum length of
blanket,
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21. Let us vary the length of blanket as
25 m, 75 m, 100 m, 125 m, 151.78
AND infinite, and calculate the
values of Xr , h0 and % reduction in
the discharge.
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22. Sample calculations for
blanket length x =50 m, are
given below
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24. The results for other values of x are
tabulated below.
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