Assuming the transition to turbulence for flow over a flat plate happens at a Reynolds number of 5x105, determine the following for air at 300 K and engine oil at 380 K. Assume the free stream velocity is 3 m/s. a. The distance from the leading edge at which the transition will occur b. Expressions for the momentum and thermal boundary layer thicknesses as a function of x for a laminar boundary layer c. Which fluid has the higher heat transfer
Given:
Assuming the transition to turbulence for flow over a flat plate happens at a Reynolds number of 5x105, determine the following for air at 300 K and engine oil at 380 K. Assume the free stream velocity is 3 m/s.
To Find:
a. The distance from the leading edge at which the transition will occur.
b. Expressions for the momentum and thermal boundary layer thicknesses as a function of x for a laminar boundary layer
c. Which fluid has a higher heat transfer
Calculation:
The transition from the lamina to turbulent begins when the critical Reynolds
number reaches [tex]5\times 10^5[/tex]
[tex](a). \;\text{Rex}_{cr}=5 \times 10^5\\\\\frac{\rho\;vx}{\mu}=5 \times 10^5\\\text{density of of air at}\;300K=1.16 \frac{kg}{m\cdot s}\\\text{viscosity of of air at}\;300K=1.846 \times 10^{-5} \frac{kg}{m\cdot s} \\v=3m/s\\\Rightarrow x=\frac{5\times 10^5 \times 1.846 \times 10^{-5} }{1.16 \times 3} =2.652 \;m \;\text{for air}\\(\text{similarly for engine oil at 380 K for given}\; \rho \;\text{and} \;\mu)\\[/tex]
[tex](b).\; \text{For the lamina boundary layer momentum boundary layer thickness is given by}:\\\frac{\delta}{x} =\frac{5}{\sqrt{R_e}}\;\;\;\;\quad\text{for}\; R_e <5 \times 10^5\\\\\text{for thermal boundary layer}\\\delta _t=\frac{\delta}{{P_r}^{\frac{1}{3}}}\quad\quad \text{where} \;P_r=\frac{C_p\mu}{K}\\\Rightarrow \delta_t=\frac{5x}{\sqrt{R_e}{P_r}^{\frac{1}{3}}}[/tex][tex](c). \frac{\delta}{\delta_t}={P_r}^{\frac{r}{3}}\\\text{For air} \;P_r \;\text{equivalent 1 hence both momentum and heat dissipate with the same rate for oil}\; \\P_r >>1 \text{heat diffuse very slowly}\\\text{So heat transfer rate will be high for air.}\\\text{Convective heat transfer coefficient will be high for engine oil.}[/tex]
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Using the formula XC=1/(2πfC) in your answer, how would a capacitor influence a simple DC series circuit?
The capacitive reactance of a DC series circuit increases when its capacitance decreases and vice-versa.
What is a DC series circuit?A DC series circuit can be defined as a type of circuit in which all of its resistive components are connected end to end, so as to form a single path for the flow of current.
This ultimately implies that, the same amount of current flows through a direct current (DC) series circuit.
The capacitive reactance of a DC series circuit.Mathematically, the capacitive reactance of a DC series circuit is given by this formula:
[tex]X_C = \frac{1}{2\pi fC}[/tex]
Where:
is the capacitive reactance.f is the frequency.C is the capacitance.From the above formula, we can deduce that the capacitive reactance of a DC series circuit is inversely proportional to both frequency and capacitance. Thus, the capacitive reactance of a DC series circuit increases when its capacitance decreases and vice-versa.
In conclusion, a capacitor would influence a simple DC series circuit by blocking the flow of direct current (DC) through it.
Read more on capacitance here: https://brainly.com/question/22989451
