A water intake at a pump storage reservoir (the fugure) has a cross-sectional ar

Question

A water intake at a pump storage reservoir (the fugure) has a cross-sectional area of 0.618 m2. The water flows in at a speed of 0.499 m/s. At the generator building, at distance D = 130 m below the intake point, the cross-sectional area is smaller than at the intake and the water flows out at 9.34 m/s. What is the difference in pressure, in megapascals, between inlet and outlet?

Explanation / Answer

(1/2)·v² + g·h + p/? = constant => (1/2)·v_i² + g·h_i + p_i/? = (1/2)·v_o² + g·h_o + p_o/? (_i denotes inlet _o outlet) => (p_i - p_o) = ?·( (1/2)·(v_o² - v_i²) + g·(h_o - h_i) ) with D = h_i - h_o (p_i - p_o) = ?·( (1/2)·(v_o² - v_i²) - g·D ) = 1000kg/m³·( (1/2)·((9.34m/s)² - (0.499m/s)²) - 9.81m/s²·130m ) = 1.23 Mpa

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