Chapter 5, Problem 5.28P

(a)

Interpretation Introduction

Interpretation:

The value of the angle ${\theta }_1$ such that the flow entering the pump is parallel to its vanes is to be determined.

Concept Introduction:

The parameters used to define a cartesian coordinate system are $x,y,\text{ and }z$ , where x defines the distance on x -axis, y defines the distance on y -axis, and z defines the distance on z -axis.

The parameters used to define a cylindrical coordinate system are $r,\theta ,\text{ and }z$ , where r defines the radial distance from the point of reference, $\theta$ defines the direction of the point from the reference point, and z defines the perpendicular distance.

The relationship between $x,y,z$ and $r,\theta ,z$ are:

  $\begin{array}{c}x=r\cos \theta \\ y=r\sin \theta \\ z=z\end{array}$

(b)

Interpretation Introduction

Interpretation:

The axial load on the shaft is to be determined.

Concept Introduction:

The general equation written for the overall linear momentum balance for a controlled volume is:

  ${\displaystyle \sum F}={\displaystyle {\iint }_{C.S}v\rho \left(v\cdot n\right)dA}+\frac{\partial }{\partial t}{\displaystyle {\iiint }_{C.V}\rho vdV}$

..... (1)

Here, C.S is the control surface over which the integral dA is taken, C.V is the control volume over which the integral dV is taken, $\rho$ is the density of the fluid, $v$ is the velocity vector, $n$ is the direction of the vector $v$ , The product $v\cdot n$ is scalar defined as:

  $v\cdot n=\left|v\right|\left|n\right|\cos \theta$