Water flows steadily through a horizontal pipe whose cross-sectional area decreases from 4A to A. If the speed in the wider part is v and losses are negligible, the pressure difference $P_wide-P_narrow$ is:
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Question

Water flows steadily through a horizontal pipe whose cross-sectional area decreases from 4A to A. If the speed in the wider part is v and losses are negligible, the pressure difference $P_wide-P_narrow$ is:

Options

G1 Physics · Accepted Answer

Continuity gives v_narrow=4v. Bernoulli at equal height: P_w+½ρv²=P_n+½ρ(4v)². Hence P_w−P_n=½ρ(16−1)v²=(15/2)ρv².

Water flows steadily through a horizontal pipe whose cross-sectional area decreases from 4A to A. If the speed in the wider part is v and losses are negligible, the pressure difference P_wide−P_narrow is: