Problem 2 Now, the AlaskaBreez group is interested in a detailed analysis of how well their spherical igloo

5. The supersoaker water gun can shoot water more than 30 ft horizontally. Estimate the minimum amount of pressure needed in the chamber to accomplish this.

Use your own words to define Alternative Fuel Vehicles (AFVS).

Multiple problems. A high efficiency impeller with 4 baffles each Dt/J=12 with Dt=1.83m=H and Da=0.61m, runs at 100 rpm with a fluid of 50 cP and 1000 kg/m3. In order to double the volume of the system and scale by equal rates of mass transfer, the new rpm is closest to: A) 86 B) 50 C) 200 D) 114 E) 126.

Consider the potential function O(x,y)=(1/3) x^3 - xy^2 +2 . Find 4(1.5,0.5); closest to A) 1.08 B) 5 C) -5 D) -1.08 E) 0.

Use your own words to explain Transit-Oriented Development (TOD).

Which is not true about boundary layer (Blasius) theory? A) assists in finding coefficients for Cd, drag coefficient B) stream function w is used to combine dependent variables C) conditions represent large dP/dx, v=0, no-slip D) thickness 6 defines where u/U(inf) = 0.99 E) n indep variable is used to combine x and y along with physical properties of system

In polymer extrusion processes, a viscous polymer of viscosity u is forced to flowsteadily from left to right (distance L) in the annular area between two fixedconcentric cylinders by applying a pressure difference Pout - Pin. The inner cylinderis solid, whereas the outer one is hollow; their radii are R1 and R2, respectively.The problem, which could occur in the extrusion of plastic tubes, is to find thevelocity profile in the annular space and the total volumetric flow rate Q. Note thatcylindrical coordinates are now involved. (a) Giving reasons, simplify the continuity equation at steady state using cylindricalcoordinates \frac{\partial \rho}{\partial t}+\frac{1}{r} \frac{\partial}{\partial r}\left(\rho r v_{r}\right)+\frac{1}{r} \frac{\partial}{\partial \theta}\left(\rho v_{\theta}\right)+\frac{\partial}{\partial z}\left(\rho v_{z}\right)=0 (b) Giving reasons, simplify the Navier-Stokes equations for the velocity component which is not zero. \rho\left(\frac{\partial v_{r}}{\partial t}+v_{r} \frac{\partial v_{r}}{\partial r}+\frac{v_{\theta}}{r} \frac{\partial v_{r}}{\partial \theta}+v_{z} \frac{\partial v_{r}}{\partial z}-\frac{v_{\theta}^{2}}{r}\right)=-\frac{\partial p}{\partial r}+\mu\left[\frac{\partial}{\partial r}\left(\frac{1}{r} \frac{\partial}{\partial r}\left(r v_{r}\right)\right)+\frac{1}{r^{2}} \frac{\partial^{2} v_{r}}{\partial \theta^{2}}+\frac{\partial^{2} v_{r}}{\partial z^{2}}-\frac{2}{r^{2}} \frac{\partial v_{\theta}}{\partial \theta}\right]+\rho g_{r} \rho\left(\frac{\partial v_{\theta}}{\partial t}+v_{r} \frac{\partial v_{\theta}}{\partial r}+\frac{v_{\theta}}{r} \frac{\partial v_{\theta}}{\partial \theta}+v_{z} \frac{\partial v_{\theta}}{\partial z}+\frac{v_{r} v_{\theta}}{r}\right)=-\frac{1}{r} \frac{\partial p}{\partial \theta}+\mu\left[\frac{\partial}{\partial r}\left(\frac{1}{r} \frac{\partial}{\partial r}\left(r v_{\theta}\right)\right)+\frac{1}{r^{2}} \frac{\partial^{2} v_{\theta}}{\partial \theta^{2}}+\frac{\partial^{2} v_{\theta}}{\partial z^{2}}+\frac{2}{r^{2}} \frac{\partial v_{r}}{\partial \theta}\right]+\rho g_{\theta} \rho\left(\frac{\partial v_{z}}{\partial t}+v_{r} \frac{\partial v_{z}}{\partial r}+\frac{v_{\theta}}{r} \frac{\partial v_{z}}{\partial \theta}+v_{z} \frac{\partial v_{z}}{\partial z}\right)=-\frac{\partial p}{\partial z}+\mu\left[\frac{1}{r} \frac{\partial}{\partial r}\left(r \frac{\partial v_{z}}{\partial r}\right)+\frac{1}{r^{2}} \frac{\partial^{2} v_{z}}{\partial \theta^{2}}+\frac{\partial^{2} v_{z}}{\partial z^{2}}\right]+\rho g_{z} (c) State the two boundary conditions needed to solve the simplified Navier-Stokes equations from (b). (d) Assuming negligible gravity effects, solve the equation derived in (b) subjected to the boundary conditions from (c) to show that the velocity profile of the viscous polymer flowing horizontally along the annulus is given by: u_{\mathrm{z}}=\frac{1}{4 \mu}\left(\frac{P_{O U T}-P_{I N}}{L}\right)\left[r^{2}-R_{1}^{2}+\frac{R_{1}^{2}-R_{2}^{2}}{\ln \left(\frac{R_{1}}{R_{2}}\right)} \ln \left(\frac{R_{1}}{r}\right)\right] (e) Derive an expression for the shear force (i.e., friction F,) arising from the shearing stress between the fluid flow (z-direction) and the external cylinder radial surface wall (r-direction).

5- Air at 290 K is compressed from 101.3 kN/m² to 2065 kN/m² in a two-stage compressor operating with a mechanical efficiency of 85 per cent. The relation between pressure and volume during the compression stroke and expansion of the clearance gas is PV^125 = constant.The compression ratio in each of the two cylinders is the same, and the inter-stage cooler maybe assumed 100 per cent efficient. If the clearances in the two cylinders are 4 per cent and 5 per cent respectively, calculate: (a) the work of compression per kg of air compressed; (b) the isothermal efficiency; (c) the isentropic efficiency (y = 1.4), and (d) the ratio of the swept volumes in the two cylinders.

2. Some diffusion problems in the atmosphere: [8 pts] a. A point source of 1000 g of SO₂ is released. If molecular diffusion (D = 0.12 cm²/s) takes place, (1) how long will it take to reach a standard deviation of 1 cm, 1 m and 100 m respectively, and (2) what are the maximum concentrations at these times? [2 pts each] b. C. By contrast, the molecular diffusion coefficient for a suspension of dust (1μm diameter) in air (Brownian motion) is approximately D = 2.2 x 10° cm²/s. Estimate the times now. Compare these to problem 2(a) and comment on the behavior of smog (made up of SO₂ and dust particles and other stuff!) in inversion layers over cites in which conditions are often without turbulence. [3 pts] An actual measurement during a SO₂ experimental point source release in an inversion layer shows that the half width as measured by the 10% level (i.e., where the concentration is 10% of the center point concentration) is 10 m at 1 hour after the release (see sketch). Estimate the diffusivity. Are these molecular conditions (compare to 2(a))? [3 pts] 021 44 Sxfel 10 m