Hello good evening Sir,Permission, i have a question in my homework. The following bellow is question. Please advice. Thank youRegards,Irfan"do an analysis of the case" EXAMPLE 11.1ХАМBasic Difference Between a Pump and a TurbineGIVEN The rotor shown in Fig. Ell1.la rotates at a con-stant angular velocity of w = 100 rad/s. Although the fluid ini-tially approaches the rotor in an axial direction, the flowacross the blades is primarily radial (see Fig. 11.la). Measure-ments indicate that the absolute velocity at the inlet and outletare V = 12 m/s and V2 = 25 m/s, respectively.A= 60°(2)(2) 2=0.2m(1)-0.1m- 100 rad/sFIND Is this device a pump or a turbine?-BladeSOLUTIONTo answer this question, we need to know if the tangentialcomponent of the force of the blade on the fluid is in the direc-tion of the blade motion (a pump) or opposite to it (a turbine).We assume that the blades are tangent to the incoming relativevelocity and that the relative flow leaving the rotor is tangentto the blades as shown in Fig. E11.1b. We can also calculate(a)IFIGU RE E11.1U2 = 20 m/sU2 = 20 m/sW230OutletBladeB2 = 60°V2 = 25 m/smotionW2/60(2)RadialKnown quantitiesshown in colorU = 10 m/sCircumferentialW1Uj = 10 m/sInletV1 = 12 m/sW1(b)(c)IFIGU RE E11.1(Continued)radial-flow turbine. In this case (Fig. E.11.1d) the flow direc-tion is reversed (compared to that in Figs. E.11.la, b, and c)and the velocity triangles are as indicated. Stationary vanesaround the perimeter of the rotor would be needed to achieveV, as shown. Note that the component of the absolute velocity,the inlet and outlet blade speeds asU = wr¡ = (100 rad/s)(0.1 m) = 10 m/sandU2 = wr2 = (100 rad/s)(0.2 m) = 20 m/sV, in the direction of the blade motion is smaller at the outletthan at the inlet. The blade must push against the fluid in thedirection opposite the motion of the blade to cause this. Hence(by equal and opposite forces), the fluid pushes against theblade in the direction of blade motion, thereby doing work onWith the known absolute fluid velocity and blade velocity atthe inlet, we can draw the velocity triangle (the graphical repre-sentation of Eq. 11.1) at that location as shown in Fig. El1.lc.Note that we have assumed that the absolute flow at the bladethe blade. There is a transfer of work from the fluid to therow inlet is radial (i.e., the direction of V, is radial). At the out-let we know the blade velocity, U2, the outlet speed, V2, and therelative velocity direction, B2 (because of the blade geometry).Therefore, we can graphically (or trigonometrically) con-struct the outlet velocity triangle as shown in the figure. Bycomparing the velocity triangles at the inlet and outlet, it can beseen that as the fluid flows across the blade row, the absolute ve-locity vector turns in the direction of the blade motion. At the in-let there is no component of absolute velocity in the direction ofrotation; at the outlet this component is not zero. That is, theblade pushes the fluid in the direction of the blade motion,thereby doing work on the fluid, adding energy to it.blade-a turbine operation.UV1U2This device is a pump.(Ans)COMMENT On the other hand, by reversing the directionof flow from larger to smaller radii, this device can become a(d)IFIGURE E11.1(Continued)

Given- A rotor is given. The inlet and outlet velocities along with the angular velocities are…

ExamPle 11.1 Basic Difference Between a Pump and a Turbine GIVEN The rotor shown in Fig. E11.la rotates at a con- stant angular velocity of w = 100 rad/s. Although the fluid ini- tially approaches the rotor in an axial direction, the flow across the blades is primarily radial (see Fig. 11.la). Measure- ments indicate that the absolute velocity at the inlet and outlet are V = 12 m/s and V2 = 25 m/s, respectively. A- 60 (2) (2) 2=0.2m (1) (1) -0.1m -100 rad/s FIND Is this device a pump or a turbine? Blade SOLUTION To answer this question, we need to know if the tangential component of the force of the blade on the fluid is in the direc- tion of the blade motion (a pump) or opposite to it (a turbine). We assume that the blades are tangent to the incoming relative velocity and that the relative flow leaving the rotor is tangent to the blades as shown in Fig. E11.1b. We can also calculate la) IFIGURE E11.1 U2 = 20 m/s U2 = 20 m/s W2 Outlet Bz = 60° Blade motion V2 = 25 m/s W2 60 (2) Radial Uj = 10 m/s Known quantities shown in color * (1) Circumferential W U1 = 10 m/s Inlet V = 12 m/s W1 (b) (e) IFIGURE E11.1 (Continued) radial-flow turbine. In this case (Fig. E.11.ld) the flow direc- tion is reversed (compared to that in Figs. E.11.la, b, and c) and the velocity triangles are as indicated. Stationary vanes around the perimeter of the rotor would be needed to achieve V, as shown. Note that the component of the absolute velocity, the inlet and outlet blade speeds as U, = wr¡ = (100 rad/s)(0.1 m) = 10 m/s and Uz = wr2 = (100 rad/s)(0.2 m) = 20 m/s V, in the direction of the blade motion is smaller at the outlet With the known absolute fluid velocity and blade velocity at the inlet, we can draw the velocity triangle (the graphical repre- than at the inlet. The blade must push against the fluid in the direction opposite the motion of the blade to cause this. Hence (by equal and opposite forces), the fluid pushes against the sentation of Eq. 11.1) at that location as shown in Fig. El1.lc. blade in the direction of blade motion, thereby doing work on Note that we have assumed that the absolute flow at the blade the blade. There is a transfer of work from the fluid to the blade-a turbine operation. row inlet is radial (i.e., the direction of V, is radial). At the out- let we know the blade velocity, U2, the outlet speed, V,, and the relative velocity direction, B2 (because of the blade geometry). Therefore, we can graphically (or trigonometrically) con- struct the outlet velocity triangle as shown in the figure. By comparing the velocity triangles at the inlet and outlet, it can be seen that as the fluid flows across the blade row, the absolute ve- locity vector turns in the direction of the blade motion. At the in- let there is no component of absolute velocity in the direction of rotation; at the outlet this component is not zero. That is, the blade pushes the fluid in the direction of the blade motion, thereby doing work on the fluid, adding energy to it. U This device is a pump. (Ans) COMMENT On the other hand, by reversing the direction of flow from larger to smaller radii, this device can become a IFIGU RE E11.1 (Continued)