A thermocouple, with a spherical junction diameter of 0.5 mm, is used for measuring the temperature of hot airflow in a circular
duct. The convection heat transfer coefficient of the airflow can be related with the diameter (D) of the sphere and the average airflow velocity (V) as h = 2.2(V /D)0.5, where D, h, and V are in m, W/m²•K, and m/s, respectively. The properties of the thermocouple junction are k = 35 W/m•K, rho = 8500 kg/m³, and cp = 320 J/kg•K.
If the maximum response time of the thermocouple to record 87 percent of the initially applied temperature difference is 5 s, determine the minimum airflow velocity that the thermocouple can be used.
If the maximum response time of the thermocouple to record 87 percent of the initially applied temperature difference is 5 s, determine the minimum airflow velocity that the thermocouple can be used.
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Answer:
The maximum theoretical height that the pump can be placed above liquid level is
Explanation:
To pump the water, we need to avoid cavitation. Cavitation is a phenomenon in which liquid experiences a phase transition into the vapour phase because pressure drops below the liquid's vapour pressure at that temperature. As a liquid is pumped upwards, it's pressure drops. to see why, let's look at Bernoulli's equation:
( stands here for density,
for height)
Now, we are assuming that there aren't friction losses here. If we assume further that the fluid is pumped out at a very small rate, the velocity term would be negligible, and we get:
This means that pressure drop is proportional to the suction lift's height.
We want the pressure drop to be small enough for the fluid's pressure to be always above vapour pressure, in the extreme the fluid's pressure will be almost equal to vapour pressure.
That means:
We insert that into our last equation and get:
And that is the absolute highest height that the pump could bear. This, assuming that there isn't friction on the suction pipe's walls, in reality the height might be much less, depending on the system's pipes and pump.