JEE221 Tutorial 3 - Solutions PDF

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TUTORIAL 3...

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JEE221 Fluid Mechanics Tutorial 3 Comprehension Questions: 5-1C: Does the amount of mass entering a control volume have to be equal to the amount of mass leaving during an unsteady flow process? No. The amount of mass or energy entering a control volume does not have to be equal to the amount of mass or energy leaving during an unsteady flow process. However, if the process is steady the two mass flow rates must be equal, otherwise the amount of mass would have to increase or decrease inside the control volume, which would make it unsteady. 9-1C: Explain the fundamental differences between a flow domain and a control volume. A control volume is used in an integral, control volume solution. It is a volume over which all mass flow rates, forces, etc. are specified over the entire control surface of the control volume. In a control volume analysis, we do not know or care about details inside the control volume. Rather, we solve for gross features of the flow such as net force acting on a body. A flow domain, on the other hand, is also a volume, but is used in a differential analysis. Differential equations of motion are solved everywhere inside the flow domain, and we are interested in all the details inside the flow domain.

Numerical Questions (Integral Form): 5-6: A hair dryer is basically a duct of constant diameter in which a few layers of electric resistors are placed. A small fan pulls the air in and forces it through the resistors where it is heated. If the density of air is 1.20 kg/m3 at the inlet and 1.05 kg/m3 at the exit, determine the percent increase in the velocity of air as it flows through the hair dryer.

5-12: The minimum fresh air requirement of a residential building is specified to be 0.35 air changes per hour. That is, 35% of the entire air contained in a residence should be replaced by fresh outdoor air every hour. If the ventilation requirement of a 2.7 m high, 200 m2 residence is to be met entirely by a fan, determine the flow capacity in L/min of the fan that needs to be installed. Also determine the minimum diameter of the duct if the average air velocity is not to exceed 5 m/s.

Water of constant density enters a conical pit through inlets at 1 and 2 and leaves through an outlet at 3. The pit is 3m deep and has a diameter of 4m at the top. If the pit is initially empty, after 5 mins, determine: a. The volumetric filling rate; (Q = -0.0228 m3/s) b. The height h of water in the pit; and (2.45 m) c. The speed at which the water level is rising in the pit. (2.72 mm/s) Apply the integral form of the continuity to answer these questions. Note the volume of a partially filled cone is given by V (h ) =

π R2H  h 

3

  H

3

D = 2R = 4 m Inlet 1 (Water In) ∅1=2R1=200mm 1

Inlet 2 (Water In)

Air

kg/min 2

m/s, with r 1 in m

Water

3

h

Outlet (Water Out) m/s, R3 =100mm

Numerical Questions (Differential Form): 9-29: Consider the following steady, three-dimensional velocity field, where a, b, c and d are constants. Under what conditions is the flow field incompressible? � � = (฀฀, ฀฀, ฀฀) = �฀฀฀฀฀฀฀ ฀ − ฀฀�  −฀฀฀฀฀฀฀฀฀฀ ฀฀ ฀฀฀฀฀฀฀฀ + ฀฀

9-35: The u velocity component of a steady, two-dimensional, incompressible flow field is ฀ ฀ = ฀฀฀฀ + ฀฀, where a and b are constants. Velocity component v is unknown. Generate an expression for v as a function of x and y....