The temperature in a 1-D bar is described by the diffusion equation, \frac{\partial u}{\partial t}=\alpha^{2} \frac{\partial^{2} u}{\partial x^{2}} Where a = (10+YZ) and YZ is the last two digits of your URN. If your URN is 6835725 then YZ =25. The problem has the following boundary and initial conditions: B C s:\left\{\begin{array}{l}

From Gerhart Flow of a viscous fluid over a flat plate surface results in the development of a region of reduced velocity adjacent to the wetted surface as depicted in Fig. P5.25. This region of reduced flow is called a boundary layer. At the leading edge of the plate, the velocity profile may be considered uniformly distributed with a value U. All along the outer edge of the boundary layer, the fluid velocity component parallel to the plate surface is also U. If the x-direction velocity profile at section(2) is \frac{u}{U}=\frac{3}{2}\left(\frac{y}{\delta}\right)-\frac{1}{2}\left(\frac{y}{\delta}\right)^{3} develop an expression for the volume flow rate through the edge of the boundary layer from the leading edge to a location downstream at x where the boundary layer thickness is 6.Figure P5.25 1) 5.25 – assume a width 'l' into the paper

5) 5.63 Water is sprayed radially outward over 180° as indicated in Fig. P5.67. The jet sheet is in the horizontal plane. If the jet velocity at the nozzle exit is 20 ft/s, determine the direction and magnitude of the resultant horizontal anchoring force required to hold the nozzle in place.

Fluids of viscosities µ ₁ = 0.1 N.s/m² and µ ₂ =0.15 N.s/m² are contained between two plates(each plate is 1 m² in area). The thicknesses are h₁ = 0.5 mm and h₂ = 0.3 mm, respectively.Find the force F to make the upper plate move at a speed of 1 m/s. What is the fluid velocity at the interface between the two fluids?

A tank, which is open to the atmosphere, is filled with water to a level h and allowed to drain through an orifice at the bottom, as shown in the figure below. The cross-sectional area of the tank is At and the cross-sectional area of the orifice is Ag. Assume that the cross-sectional area of the tank is much greater than the cross-sectional area of the orifice (AT>>Ao) and that the exit losses are negligible. 6) Use Reynolds Transport Theorem to derive an expression for the variation of h with time as a function of velocity at the outlet.

*5-96. Determine the power delivered to the turbine if the water exits the 400-mm-diameter pipeat 8 m/s. Draw the energy and hydraulic grade lines for the pipe using a datum at point C.Neglect all losses.

3) 5.45 Determine the magnitude and direction of the anchoring force needed to hold the horizontal elbow and nozzle combination shown in Fig. P5.47 in place. Atmospheric pressure is 100 kPa(abs). The gage pressure at section (1) is 100 kPa. At section (2), the water exits to the atmosphere.

Launch Meeting-Zoum5-111. A fire truck supplies 150 gal/min of water to the third story of a building at B. If the frictionloss through the 60-ft-long, 2.5-In.-diameter hose is 12 ft for every 100 ft of hose, determine therequired pressure developed at the outlet A of the pump located within the truck close to theground. Also, what is the average velocity of the water as it is ejected through a 1.25-in.-diameter nozzle at B?

10) A conveyor belt discharges gravel onto a barge at a rate of 50 yd/min. If the gravel weighs 120 Ibf/ft^3, what is the tension in the hawser that secures the barge to the dock?

10.2-39 The following vapor-liquid equilibrium data havebeen reported' for the system water (1) + 1,4-dioxane (2) at 323.15 K. Compute the activity coefficients for thissystem at each of the reported compositions.a. b. Are these data thermodynamically consistent? c. Plot the excess Gibbs energy for this system asa function of composition.

"5-104. The flow of air at A through a 200-mm-diameter duct has an absolute inlet pressure of180 kPa, a temperature of 15°C, and a velocity of 10 m/s. Farther downstream a 2-kW exhaustsystem increases the outlet velacity at B to 25 m/s. Determine the change in enthalpy of the air.Neglect heat transfer through the pipe.B