In an inviscid, incompressible flow of air along a streamline, the air density is 0.002377 slug/ft^3. Find the pressure at a point.
In an inviscid, incompressible flow of air along a streamline, the air density is 0.002377 \({\rm{slug/f}}{{\rm{t}}^{\rm{3}}}\). At a point on the streamline pressure and velocity are 2000 \({\rm{lb/f}}{{\rm{t}}^{\rm{2}}}\) and 15 ft/s, respectively. Downstream at other point on the streamline the velocity is 150 ft/s. What is the pressure at this point.
From, Bernoulli’s equation\[{p_1} + \frac{1}{2}\rho v_1^2 = {p_2} + \frac{1}{2}\rho v_2^2\]\[{p_2} = {p_1} + \frac{1}{2}\rho \left( {v_1^2 – v_2^2} \right)\]\[{p_2} = 2116 + \frac{1}{2}\left( {0.002377} \right)\left[ {{{\left( {15} \right)}^2} – {{\left( {150} \right)}^2}} \right]\]\[ = 2089.526\,\,lb/f{t^2}\]
