Water flows horizontally from speed \(2.0\,\mathrm{m\,s^{-1}}\) to \(5.0\,\mathrm{m\,s^{-1}}\). Find \(p_1-p_2\).

Water is accelerated from a very wide, nearly stationary region into a horizontal pipe by a pressure drop of \(18\,\mathrm{kPa}\). Find the pipe speed.

A small hole is \(0.80\,\mathrm{m}\) below the surface of a large open water tank. Estimate the exit speed.

A liquid flows steadily with the same speed at two points. Point 2 is \(3.0\,\mathrm{m}\) higher than point 1. For water, find \(p_1-p_2\).

Water flows horizontally through a constriction where the area halves. If \(v_1=1.5\,\mathrm{m\,s^{-1}}\), find \(v_2\) and \(p_1-p_2\).

Water flows from point 1 to point 2. The speed changes from \(2.0\,\mathrm{m\,s^{-1}}\) to \(3.0\,\mathrm{m\,s^{-1}}\), and point 2 is \(4.0\,\mathrm{m}\) higher. Find \(p_1-p_2\).

A Pitot-style measurement in air of density \(1.2\,\mathrm{kg\,m^{-3}}\) gives stagnation pressure \(540\,\mathrm{Pa}\) above static pressure. Find the air speed.

A hole in a large tank is \(1.25\,\mathrm{m}\) below the water surface and \(0.80\,\mathrm{m}\) above the floor. Estimate the horizontal range of the emerging water stream.

A horizontal Venturi tube carries water. The wide area is four times the narrow area, and the wide-section speed is \(1.0\,\mathrm{m\,s^{-1}}\). Find the pressure drop from wide to narrow section.

A large open tank has a small outlet of area \(1.0\times10^{-4}\,\mathrm{m^2}\), located \(2.0\,\mathrm{m}\) below the surface. Estimate the volume flow rate from the outlet.

Water flows horizontally. At section 1, \(p_1=2.20\times10^5\,\mathrm{Pa}\) and \(v_1=2.0\,\mathrm{m\,s^{-1}}\). At section 2, \(v_2=7.0\,\mathrm{m\,s^{-1}}\). Find \(p_2\).

A water jet exits vertically upward into the atmosphere from a nozzle fed by gauge pressure \(45\,\mathrm{kPa}\). Neglect losses and inlet speed. Estimate the maximum jet height.

Explain why a horizontal ideal-fluid streamline that speeds up must move toward lower pressure. Use Bernoulli's equation and also state the force interpretation.

A horizontal pipe carries a liquid of unknown density. The speed increases from \(1.0\,\mathrm{m\,s^{-1}}\) to \(4.0\,\mathrm{m\,s^{-1}}\), and the pressure falls by \(6.0\,\mathrm{kPa}\). Find the density implied by Bernoulli's equation.

A siphon carries water from a large open reservoir to an outlet \(1.5\,\mathrm{m}\) below the reservoir surface. The siphon crest is \(0.80\,\mathrm{m}\) above the reservoir surface. Neglect losses and pipe-radius changes. Estimate the absolute pressure at the crest.

A horizontal streamline has speed \(v(s)\) along distance coordinate \(s\). Starting from Bernoulli's equation, derive \(dp/ds\) in terms of \(v\) and \(dv/ds\). Interpret the sign when the flow accelerates.

For horizontal incompressible flow, section 1 has area \(A_1\), speed \(v_1\), and pressure \(p_1\). Section 2 has area \(A_2\). Derive \(p_1-p_2\) in terms of \(\rho\), \(v_1\), and \(k=A_1/A_2\).

A tank surface area \(A_T\) is not extremely large compared with a hole area \(a\). The water surface is height \(h\) above the hole, and both surface and hole are open to the atmosphere. Derive the hole speed using continuity and Bernoulli.

A horizontal constriction has \(A_1/A_2=k>1\). Upstream pressure is \(p_1\), vapor pressure is \(p_v\), and density is \(\rho\). Derive the maximum upstream speed \(v_1\) that keeps the narrow-section pressure at or above \(p_v\).

A streamline connects points 1 and 2 in steady incompressible nonviscous flow. Derive a symbolic condition, using only \(p_1-p_2\), \(y_2-y_1\), and \(\rho\), for point 2 to have a larger speed than point 1. Interpret the condition physically.