1 during a plant visit it was noticed that a 12 m long...

During a plant visit, it was noticed that a 12 m long section of a 10 cm diameter steam pipe is completely exposed to the ambient air. The temperature measurements indicate that the average temperature of the outer surface of the steam pipe is 75°C when the ambient temperature is 5°C. There are also light winds in the area at 10 km/h. The emissivity of the outer surface of the pipe is 0.8, and the average temperature of the surfaces surrounding the pipe, including the sky, is estimated to be 0°C. Determine the amount of heat lost from the steam during a 10-hour-long work day. Steam is supplied by a gas-fired steam generator that has an efficiency of 80 percent, and the plant pays $1.05/therm of natural gas. If the pipe is insulated and 90 percent of the heat loss is saved, determine the amount of money this facility will save a year as a result of insulating the steam pipes. Assume the plant operates every day of the year for 10 hours. State your assumptions.

Transcript

00:01 Given the length which is equal to the 90 meter we are given the diameter which is 6 .03 centimeter we are given the initial time yeah time at 1 which is 170 degree celsius or we can say that 443 kelvin and we are given the time infinity temperature at infinity which is equals to the 20 degrees celsius or we can say that 293 kelvin and at value of epsilon is also given which is 0 .7 the value of meter is given which is 0 .7 the value of and we have given the value of c unit which is cost of unit which is 1 .10 per third.

00:40 So we have to write the expression for film temperature.

00:46 So from here expression for film temperature is t f is equal to t1 plus t infinity divides by the two.

00:54 So so here we after putting all the values we get the value of t of f as 19.

01:00 Degrees celsius.

01:01 So this is the answer for the value of 2 t of f.

01:06 Now we have we write the property for air at air at 95 degrees celsius.

01:13 So here the value of k is given which is 0 .030950 .5.

01:21 And the value of new is given which is 2 .2526 multiplies by 10 raised to the power minus 5 meter square per second.

01:30 So here we can write it as that p of r is equal to 0 .70527 and the expression for beta is here is that beta is equal to 1 divided by the t of f.

01:42 So from here we can substitute the value of t of f here in the beta which is equal to the beta is equal to 1 divides by a 95 degree.

01:50 So from here we can say that beta is equal to 0 .002717 calving inverse.

01:57 So this is the value here for the b2 ,000.

02:01 Now we have to find now we have to find out that we know that delta t is equal to t i minus t at infinity.

02:15 So here the delta t comes out to be 150 kelvin after putting the values of t and i and t here so from here we get the value of delta t now we have to find out the expression for rate lake's number of this lender is r of a b is equal to g beta delta t d cube p r divides by a v square so after putting all these values here in the r ad we get the value of r ad as 1 .21 851 multiplies by the 10 is to the power 6 so this is the value for the r ad now we expression for nacelle number so expression for neselt number is that and you here represent neselt number which is equal to 0 .6 plus 0 .378 r a d raised to the power 1 divides by the 6 divides by 1 plus 0 .559 divides by the pr raised to the power 9 divides by the 16 whole whole raise to the power is 8 divides by a 27 raised to the power 2 so after after putting all these values here we get the value of nu as 14 .76.

03:35 So this is the value for the nessler's number and we can write it as that nh is also equals to hd divides by the k...

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