A liquid (ρ=1.65 g / cm^3 ) flows through a horizontal pipe...

A liquid $(\rho=1.65 \mathrm{g} /$ $\mathrm{cm}^{3}$ ) flows through a horizontal pipe of varying cross section as in Figure $\mathrm{P9} .36$ In the first section, the cross-sectional area is 10.0 $\mathrm{cm}^{2}$ the flow speed is $275 \mathrm{cm} / \mathrm{s},$ and the pressure is $1.20 \times$ $10^{5}$ Pa. In the second section, the cross-sectional area is 2.50 $\mathrm{cm}^{2}$ . Calculate the smaller section's (a) flow speed and (b) pressure.

A liquid $(\rho=1.65 \mathrm{g} /$ $\mathrm{cm}^{3}$ ) flows through a horizontal pipe of varying cross
section as in Figure $\mathrm{P9} .36$ In the first section, the cross-sectional area is 10.0 $\mathrm{cm}^{2}$ the flow speed is $275 \mathrm{cm} / \mathrm{s},$ and the pressure is $1.20 \times$ $10^{5}$ Pa. In the second section, the cross-sectional area is 2.50 $\mathrm{cm}^{2}$ . Calculate the smaller section's (a) flow speed and (b) pressure.

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Key Concepts

Incompressible Flow

Incompressible flow assumes that the density of the fluid remains constant throughout the flow. This assumption is essential when applying both the continuity equation and Bernoulli's equation since it ensures that variations in pressure and velocity are directly related without changes in fluid density.

Bernoulli's Equation

Bernoulli's equation represents the conservation of energy along a streamline in steady, incompressible flow. It relates the fluid's pressure, kinetic energy per unit volume, and potential energy per unit volume. In horizontal flows where elevation differences can be neglected, it shows how increases in flow velocity correspond to decreases in pressure.

Continuity Equation

This principle states that for an incompressible fluid the mass flow rate must be constant along a streamline. In practical terms, it means that as the cross-sectional area of a pipe changes, the fluid's speed adjusts accordingly so that the product of cross-sectional area and velocity remains constant.

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