You are irrigating your backyard garden using a hose of different cross-sectional area. Suppose, the cross-sectional area of end ‘A’ of pipe is double than end ‘B’, what will be the velocity of water at end B in comparison to end A?
Added by Frank J.
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This means that the product of the cross-sectional area (A) and the velocity (V) of the fluid must be the same at both ends of the pipe. Show more…
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Two hoses are connected to the same outlet using a Y-connector, as the drawing shows. The hoses $A$ and $B$ have the same length, but hose $B$ has the larger radius. Each is open to the atmosphere at the end where the water exits. Water flows through both hoses as a viscous fluid, and Poiseuille's $\operatorname{law}\left[Q=\pi R^{4}\left(P_{2}-P_{1}\right) /(8 \eta L)\right]$ applies to each. In this law, $P_{2}$ is the pressure upstream, $P_{1}$ is the pressure downstream, and $Q$ is the volume flow rate. The ratio of the radius of hose $\mathrm{B}$ to the radius of hose $\mathrm{A}$ is $R_{\mathrm{B}} / R_{\mathrm{A}}=1.50 .$ Find the ratio of the speed of the water in hose $B$ to the speed in hose $A$.
$* .$ Go Two hoses are connected to the same outlet using a Y-connector, as the drawing shows. The hoses A and B have the same length, but hose $\mathrm{B}$ has the larger radius. Each is open to the atmosphere at the end where the water exits. Water flows through both hoses as a viscous fluid, and Poiseuille's law $\left[Q=\pi R^{4}\left(P_{2}-P_{1}\right) / 8 \eta L\right]$ applies to each. In this law, $P_{2}$ is the pressure upstream, $P_{1}$ is the pressure downstream, and $Q$ is the volume flow rate. The ratio of the radius of hose $\mathrm{B}$ to the radius of hose $\mathrm{A}$ is $R_{\mathrm{B}} / R_{\mathrm{A}}=1.50$. Find the ratio of the speed of the water in hose $\mathrm{B}$ to the speed in hose $\mathrm{A}$.
Two hoses are connected to the same outlet using a Y-connector, as the drawing shows. The hoses A and B have the same length, but hose B has the larger radius. Each is open to the atmosphere at the end where the water exits. Water flows through both hoses as a viscous fluid, and Poiseuille’s law $\left[Q=\pi R^{4}\left(P_{2}-P_{1}\right) /(8 \eta L)\right]$ applies to each. In this law, $P_{2}$ is the pressure upstream, $P_{1}$ is the pressure down- stream, and $Q$ is the volume flow rate. The ratio of the radius of hose $B$ to the radius of hose A is $R_{B} / R_{A}=1.50 .$ Find the ratio of the speed of the water in hose $\mathrm{B}$ to the speed in hose A.
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