# Find out the Discharge of a Siphon Spillway – Problem & Solution

## Find out the Discharge of a Siphon Spillway

Mathematical Problem:

Find out the discharge of a siphon spillway from following data:

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• Number of siphon units = 4
• Area at throat in m2 = 3
• Full reservoir level = 150 m
• R.L of centre of outlet = 128
• Tailwater level on D/S side during rains = 130
• Tailwater level during winter = 125
• Discharge coefficient = 0.60

Solution:

Case 1

In rainy days outlet remains submerged and hence discharge depends upon the tailwater level.

Working head = R.L of reservoir – R.L. or T.W.L. = 150 – 130 = 20 m.

$Q = CA \sqrt{2gh}$

Or, $Q = 0.60\times 3 \sqrt{2g\times 20}$

Or, Q = 35.75 cumecs.

So, the discharge of four units = 4 × 35.75 = 143 cumecs.

Case II

In winter T.W.L falls down and spillways discharge free in the air.

Available head = Reservoir level – R.L of center of outlet = 150 – 128 = 22 m.

$Q = CA \sqrt{2gh}$

Or, $Q = 0.60\times 3 \sqrt{2 \times 9.81 \times 22}$

Or, Q = 37.5 cumecs.

Discharge of four units = 4 × 37.5 = 152 cumecs.