A sharp-crested triangular weir with a notch angle of (80^{circ}) is used to measure the discharge rate

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A sharp-crested triangular weir with a notch angle of \(80^{\circ}\) is used to measure the discharge rate of water from a large lake into a spillway. If a weir with half the notch angle \(\left(\theta=40^{\circ}\right)\) is used instead, determine the percent reduction in the flow rate. Assume the water depth in the lake and the weir discharge coefficient remain unchanged.

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