A variable mesh screen produces a linear and axisymmetric velocity profile as indicated in the figure below in the air flow through a 4 - ft-diameter D circular cross-sectional duct. The static pressures upstream and downstream of the screen are p1=0.49 psi and p2=0.15 psi and are uniformly distributed over the flow cross-sectional-area. Neglecting the force exerted by the duct wall on the flowing air, calculate the screen drag force. Would an appropriate control volume be the screen with the flow entering and leaving the surfaces? Part 2 ok and Media (a) Write the momentum flux before the screen where the flow is uniform in terms of velocity V, density , and cross-sectional area A. (b) Write the velocity after the screen in terms of the maximum velocity, umax, the radius of the pipe, R, and the radial distance, r, from the centerline of the circular pipe. (c) Write the integral (take it) of the velocity after the screen over the cross-sectional area of the pipe in terms of the maximum velocity, umax and the radius of the pipe, R. (d) Write the expression for the mass flux in terms of the density , the maximum velocity, umax and the radius of the pipe, R. (e) Now, write the integral (take it) for the momentum flux after the screen in terms of the maximum velocity, umax and the radius of the pipe, R. (a) (b) (c) (d) (e) Evaluate umax and the momentum fluxes for the control volume around the screen. (a) What is the uniform velocity before the screen? V1= (b) What is the magnitude of the mass flux before the screen? m1= (c) What is the magnitude of the mass flux after the screen? m2= (d) What is the value of umax ? umax (e) What is the value of the momentum flux before the screen? R1= (f) What is the value of the momentum flux after the screen? R2= Part 4 Evaluate the external forces on the control volume. Using the convention of external forces on the right-hand side of the equation and momentum fluxes on the left-hand side w aforementioned sign conventions: (a) What is the force due to pressure before the screen? F1= (b) What is the force due to pressure after the screen? F2= (c) What is the drag force on the screen? Rx= slugs /s ft/s ft/s2 lbf/m2 slugs /s2 lbf/m lbf (d) In which direction does the drag force on the fluid act? A variable mesh screen produces a linear and axisymmetric velocity profile as indicated in the figure below in the air flow through a 4 - ft-diameter D circular cross-sectional duct. The static pressures upstream and downstream of the screen are p1=0.49 psi and p2=0.15 psi and are uniformly distributed over the flow cross-sectional-area. Neglecting the force exerted by the duct wall on the flowing air, calculate the screen drag force. Would an appropriate control volume be the screen with the flow entering and leaving the surfaces? Part 2 ok and Media (a) Write the momentum flux before the screen where the flow is uniform in terms of velocity V, density , and cross-sectional area A. (b) Write the velocity after the screen in terms of the maximum velocity, umax, the radius of the pipe, R, and the radial distance, r, from the centerline of the circular pipe. (c) Write the integral (take it) of the velocity after the screen over the cross-sectional area of the pipe in terms of the maximum velocity, umax and the radius of the pipe, R. (d) Write the expression for the mass flux in terms of the density , the maximum velocity, umax and the radius of the pipe, R. (e) Now, write the integral (take it) for the momentum flux after the screen in terms of the maximum velocity, umax and the radius of the pipe, R. (a) (b) (c) (d) (e) Evaluate umax and the momentum fluxes for the control volume around the screen. (a) What is the uniform velocity before the screen? V1= (b) What is the magnitude of the mass flux before the screen? m1= (c) What is the magnitude of the mass flux after the screen? m2= (d) What is the value of umax ? umax (e) What is the value of the momentum flux before the screen? R1= (f) What is the value of the momentum flux after the screen? R2= Part 4 Evaluate the external forces on the control volume. Using the convention of external forces on the right-hand side of the equation and momentum fluxes on the left-hand side w aforementioned sign conventions: (a) What is the force due to pressure before the screen? F1= (b) What is the force due to pressure after the screen? F2= (c) What is the drag force on the screen? Rx= slugs /s ft/s ft/s2 lbf/m2 slugs /s2 lbf/m lbf (d) In which direction does the drag force on the fluid act
