Consider the electronic elements that are cooled by forced convection in Problem 6.31. The cooling system is designed and tested at sea level (p ≈ 1 atm), but the circuit board is sold to a customer in Mexico City, with an elevation of 2250 m and atmospheric pressure of 76.5 kPa. (a) Estimate the surface temperature of the chip located 120 mm from the leading edge of the board when the board is operated in Mexico City. The dependence of various thermophysical properties on pressure is noted in Problem 6.19.

surface temperature of the chip located 120 mm Ts=42.5°C

surface temperature of the chip in Mexico Ts=46.9°C

Explanation:

from the energy balance equation we have to:

q=E=30W

from Newton´s law:

Ts=Tα+(q/(h*A)), where A=l^2

N=h/k=0.04*(Vl/V)^0.85*Pr^1/3

data given:

l=0.12 m

v=10 m/s

k=0.0269 W/(m*K)

Pr=0.703

Replacing:

h=0.04*(0.0269/0.12)*(10*0.12)/((16*69x10^-6))^0.85*(0.703^1/3) = 107 W/m^2*K

The surface temperature at sea level is equal to:

Ts=25+(30x10^-3/107*0.004^2)=42.5°C

h=0.04*(0.0269/0.12)*((10*0.12)/(21*81x10^-6))^0.85*(0.705^1/3)=85.32 W/(m*K)

the surface temperature at Mexico City is equal to:

Ts=25+(30x10^-3/85.32*0.004^2)=46.9°C

pe = weightxheight = 2000x1000=2,000,000joules

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.