Simplify the continuity equation and the Navier-Stokes equations that describe the fluid flow between two flat, parallel plates. (x-component only) The pressure drop is constant. Clearly state your reason for eliminating each term and state any assumptions you make in simplifying the equation. [DO NOT solve the differential equations.]

A Newtonian fluid in laminar flow is flowing down in inclined-plane surface (shown below).Use the shell-balance approach to (1) derive the governing differential equations. (2) State the boundary conditions for the systems. [DO NOT solve the differential equations.]

Species Accumulation and Transport within an Interface Accumulation and transport within an interface can be important for species that reside at phase boundaries, such as gases adsorbed on solids or surfactants at fluid-fluid interfaces. The objective is to derive more general interfacial conservation statements than those in Section 2.2. Consider a species that may be present at an interface or in either of the adjacent bulk phases. Let Cs and Ng be its surface concentration (moles m2) and surface flux (moles m¹s¹), respectively; note the differences in units from the corresponding three-dimensional quantities. The vector Ng is every- where tangent to the surface. (a) For part of an interface corresponding to surface S in Fig. A-2, state the macroscopic (integral) solute conservation equation. Assume that phase A is below S and phase B above it, such that n points toward the latter. Include the possibility of chemical reactions at the interface, trans- port to or from the bulk phases, and interfacial motion. The interface is not necessarily planar. (b) By reducing the integral equation of part (a) to a partial differential equation, show that at where N and C are the species flux and concentration, respectively, in a bulk phase. (Sub- scripts identifying the chemical species have been dropped for simplicity.) This result, which is valid instantaneously and locally, is equivalent to Eq. (5.2-2) of Edwards et al. (1991). How does it compare with what is obtained by applying Eq. (2.2-15) to a chemical species?

2. Problem 2.5 from the textbook. Instead assume that the co = 2 kg/m³ and Q = 0.015 m³ /s.

Calculate the viscosity (in Pars) of oxygen at 450 K using both (1) the expression derived from kinetic gas theory. (d = 0.355 nm (oxygen), Boltzmann constant = 1.3806 x 10³ m² kg s² K')For the reference, see the values reported in WRF Appendix I and K (uploaded in Canvas).

2- Consider the arrangement of a collector tank, pump and reservoir tank shown in Figure. Taking the pump pressure requirement equation from Section 8 iv: P_{p}=\frac{1}{2} \rho_{-} x_{2}^{2}+\rho_{-} g h_{2}-\rho_{-} g h_{1}+f_{h}-\rho_{q} P_{p}=\rho g \cdot\left(h_{2}-h_{1}+f_{h}\right) And assuming the kinetic energy term is negligible gives us: This is the general equation for calculating the pressure requirement for a pump. Combined with two other Equation (B) which gives the power that needs to be supplied to the pump (Win): W_{\text {in }}=P_{p} \cdot Q / \gamma which gives the electrical power required (We): W_{e}=I . V it is possible to derive the pump specification for a series of different diameter delivery pipes,assuming a given volumetric flow rate. A reservoir tank is 100m uphill from a water source, the difference in height between the two is 20 m. It is proposed to use a pump to push the water up to the reservoir tank at a flow rate of 0.5 1/s. Two pipe diameters of ½" and 1" are available to link the two. What size pumps are required (in Watts) for each pipe diameter, assuming a pump efficiency of 50% and what electrical current is required assuming the smaller pump is chosen and we are stealing the electricity from a 110 V pylon ?. we have 100m of pipe and for a flow rate of 0.51/s the frictional head loss chart gives the following results for ½" and 1" dia. pipes: Taking the density of water as p= 1000 Kg/m³ and the acceleration due to gravity as g = 9.81 m/s².

1. Estimate the optimal cycle length and green intervals for the intersection shown in the Figure below. Assume two phases A and B. Phase A serves the north-south traffic and phase B serves the east-west traffic. Lost time is 3sec/phase and Yellow+All-Red is4sec/phase. The width of each lane is 10 ft. Prevailing saturation flows are as follows: S(T+R)=1700 (flow rate for through and right) S(L) 300 (flow rate for left, which reflects a permitted operation) Assume zero grade. No. of pedestrians crossing during an interval = 10. Crosswalk width(We) = 8ft. Pedestrian walking speed = 3.5ft/s.