Hydraulic Engineering Exam Help

Hydraulic Engineering Exam Help

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Problem Problem 1 (20%) – Calculation of Flow Quality from Void Fraction Measurements By means of X-ray imaging techniques an MIT graduate student is able to measure the void fraction in the downcomer of an experimental apparatus designed to study steam carryunder at 7.0 MPa. This student has taken course 22.313, so she is also able to calculate the relative velocity, vb=vℓ-vv, from a Re-Eo-M diagram for bubbly flow. Does the student miss any information needed to calculate the flow quality in the dowcomer? (Note: in answering this question, do not assume that a carryunder correlation is available) If so, what information is missing?

If not, write a set of equations that would allow the student to calculate the flow quality given only theDrop void infraction, the relative velocity Flow and, of Problem 2 (30%) – Pressure Accelerating Single-Phase course, the properties of steam and water at 7.0 MPa. Consider upflow in a vertical section of the PWR primary system piping. i) Write the time-dependent mass and momentum conservation equations for this system, assuming that the water coolant can be treated as perfectly incompressible. (15%) ii)Now consider a transient during which the mass flux within the tube increases linearly with time, while the inlet pressure is held constant. Using the momentum equation, demonstrate that the pressure at the outlet decreases during this transient. (15%) liveexamhelper.com

Problem 3 (50%) – Sizing of a Turbulent-Deposition Air/Water Separator An engineering company is designing an air-conditioning system for a large building. An important component is the moisture separator that removes small water droplets from the conditioned air. The separator is of the turbulent-deposition type, and consists of a single horizontal tube. The deposited liquid is drained at the tube outlet (Figure 1). The separator processes an air/water mixture with mass flow rate of 0.42 kg/s and flow quality of 95%. The physical properties of water and air at the temperature and pressure of interest are reported in Table 1.

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z

Drained liquid

Figure 1. Schematic of the air/water separator. i) For the effective performance of the separator, it is essential to prevent reentrainment of the deposited liquid. Using the Ishii-Mishima correlation for the onset of entrainment, calculate the diameter of the separator that guarantees a 30% margin to re-entrainment. (15%) ii)Using the McCoy-Hanratty correlation for droplet deposition in turbulent flow, calculate the length of the separator required to reduce the moisture content of the air by 50%. (30%) iii)What is the separation efficiency of the separator? (5%) Assumptions  The water droplets move homogeneously with the air.  The liquid film on the wall is thin.

Simplified versions of the Ishii-Mishima and McCoy-Hanratty correlations are given below for your convenience: liveexamhelper.com

(Ishii-Mishima) (McCoy-Hanratty) Table 1. Properties of water and air at room temperature and atmospheric pressure.

Parameter Water ℓ ℓ  Air v v

Value 1,000 kg/m3 0.001 Pas 0.07 N/m 1.2 kg/m3 1.710-5 Pas

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Solutions Problem 1 (20%) – Calculation of Flow Quality from Void Fraction Measurements The information missing is the mass flux (or a superficial velocity) in the downcomer. For example, if the mass flux were known, then the following set of equations would enable calculation of the flow quality: (fundamental -x-S equation) (definition of slip ratio) (relative velocity; note that in general v𝑙  v v in downflow) (mass flux) Problem 2 (30%) – Pressure Drop in Accelerating SinglePhase Flow i) For a perfectly incompressible fluid the density  is constant, and so the momentum equations respectively: where Pw,mass A andand De are the channel wetted become, perimeter, flow area and equivalent diameter, respectively. ii) Integrating the momentum equation with respect to z, one gets:

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The pressure at the inlet is constant by assumption. The first term on the right-hand side is also constant because G increases linearly with time. The third term on the right-hand side is constant because the fluid is incompressible. The second term on the right-hand side increases roughly as t2. Therefore, the above equation suggests that the outlet pressure must decrease roughly as t2.

Problem 3 Separator

(50%)

–

Sizing

of

a

Turbulent-Deposition

Air/Water

i) The Ishii-Mishima correlation gives the value of the air superficial velocity at the onset of entrainment, jv=15.7 m/s (calculated with the thermophysical properties of Table 1). Thus the separator will have to operate at jv=0.715.7 m/s  11 m/s.

Then the diameter of the separator can be calculated from the following equation: where x=0.95 and m& =0.42 kg/s. ii) A mass balance for the water droplets in the vapor core (see notes on annular flow) gives:

where ‘e’ is the entrained liquid fraction (e =1 at the inlet), and Γd is the rate of droplet deposition, which can be found as:

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where K=0.1 m/s is the deposition coefficient given by the McCoy-Hanratty correlation. Integration of the mass balance equation gives:

where L is the length of the separator. If ‘e’ is to decrease by 50%, then the required length is:

iii) The separation efficiency of the separator is 50%, since 50% of the initial moisture content is removed.

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