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# 5_27 - shaft running unrestrained What is the torque T at...

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Problem 5.27 Centrifugal pump/turbine The sketch shows a centrifugal turbine or pump with an impeller in a flat-sided casing of width b . A liquid of density flows through the pump at a volume flow rate Q . Assuming that (i) the liquid enters with a purely axial velocity and (ii) exits at radius r 2 with a velocity that follows the (moving) blade surfaces, and (iii) neglecting frictional effects, (a) derive an expression for the c ounterclockwise external torque, T S , exerted on the shaft at an angular speed ϖ. Express it in terms of Q, , b, r 1 , r 2 , 1 , 2 and ϖ. ANSWER (b) What is the system’s run-away speed 0 , that is, the (counterclockwise) speed of the

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Unformatted text preview: shaft running unrestrained? What is the torque T at zero rotation? ANSWER (c) Show that your result in (a) reduces to the universal form T S T S = f ( ) and plot this function. (d) Derive the power output to the shaft, ˙ W S = T S , as a function of ϖ . At what range of values of β will the power output be positive (that is, the system be a pump), if β0? At what value(s) of ϖ / ϖ is the power output maximized? Provide expressions for the maximum power and the angular frequency at which it is attained, expressed in terms of Q, , b, r 1 , r 2 , 1 , and 2 . ANSWER...
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5_27 - shaft running unrestrained What is the torque T at...

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