Please solve part (c) and (d) ### Image Transcription for Educational Website#### Diagram ExplanationThe diagram illustrates the fluid dynamics around a cylindrical object immersed in an infinite fluid volume. The setup represents a common scenario in fluid mechanics, where an object is analyzed within a flowing fluid.#### Diagram Elements1. **Cylinder:** - Located at the center, the cylinder has a radius denoted by \( R \). - An arrow within the cylinder indicates a rotational motion with angular velocity \( \omega \).2. **Coordinate System:** - The origin is at the cylinder's center. - A radial line labeled \( r \) extends from the center outward, with an angle \( \phi \) defining its orientation.3. **Fluid Flow:** - The background flow is represented by yellow lines with arrows indicating the direction of the fluid. - The fluid is described as having infinite volume surrounding the cylinder.4. **Equations and Conditions:** - The common boundary condition \( R \leq r < \infty \) is highlighted in the boxed region. - An important note on boundary conditions as \( r \rightarrow \infty \): - \( u_r = 0 \) - \( p = p_a \) - These conditions are particularly relevant in cylindrical coordinate systems when analyzing flow.5. **Notes:** - A cautionary remark underlines the importance of these conditions that often occur in flows with cylindrical coordinates. By understanding this setup, students can learn about cylindrical flow patterns, boundary conditions, and the impact of rotational motion on the fluid dynamics around a cylinder. **Text for Educational Website:****B. Analysis of Flow in a Rotating Cylinder***Figure B* illustrates a horizontal cross-section of a long vertical cylinder with a radius \( R \). This cylinder is rotated steadily in a counterclockwise direction with an angular velocity \( \omega \) within a large volume of a Newtonian liquid characterized by viscosity \( \mu \) and density \( \rho \). The liquid is considered to extend infinitely and remain at rest. The cylinder's axis aligns with the \( z \)-axis of a cylindrical coordinate system, indicating a laminar, steady-state flow without the influence of gravity.**(a) Velocity Components of the Flow:**Identify which velocity components in a cylindrical coordinate system (\( v_r, v_\theta, v_z \)) are zero for this flow.**(b) Continuity Equation:**Formulate the continuity equation for the described flow. Compute the result and provide commentary on the implications of your analysis.**(c) Momentum Equation:**Develop the momentum equation for this flow in the axial direction. Identify which terms cancel out, discuss the results of your analysis, and interpret the significance of these findings.

Solution: solving part c)Equation of motion for Newtonian fluid of constant viscosity μ and density ρ in cylindrical coordinates are: Cylindrical coordinates (r,θ, z) components: From Handbook: Considering fluid moves in a circular pattern: velocity and pressure components become: vθ=vθ(r)vr=0vz=0p=p(r,z) Components of equation of motion simplifies to: r-component-ρvθ2r=-∂p∂r θ-component0=ddr1rddrrvθ z-component0=-∂p∂z-ρg θ-component gives velocity distribution. z-component gives effect of gravity on pressure and r-component gives information about the centrifugal force affecting the pressure. Only θ-component from the equation of motion is needed.