Question #232714

A steam pipe shown below has two sections, an expanded and contracted ends. The pressures, density, diameters and velocities of the pipe are given; fluid density ρ =960kg/m3 ,the sections diameters D1 = 100mm, D2=80mm, the gauge pressure at section one is P1 =200KN/m2 and the velocity at point one U1= 5m/s. What is the pressure at point 2?

Expert's answer

"\\frac{p_1}{\\rho g}+\\frac{u^2_1}{2 g}+z_1=\\frac{p_2}{\\rho g}+\\frac{u^2_2}{2 g}+z_2\\\\\nz_1=z_2\\\\\np_2=p_1+\\frac{\\rho}{2}(u_1^2-u_2^2)\\\\"

Use the continuity equation to find u_{2}

"A_1u_1=A_2u_2\\\\\nu_2= \\frac{A_1u_1}{A_2}= \\frac{d^2_1}{d^2_2}u_1\\\\\n= 7.8125 m\/s"

So pressure at section 2

"p_2= 200000-17296.87\\\\\n=182703 N\/m^2"

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