Question

Problem # 2 Consider an ordinary shower where hot water at $T_1 = 65 \degree C$ is mixed with cold water at $T_2 = 5 \degree C$. It is desired to steadily supply warm water at $T_3$ for the daily use. Compute the outlet temperature $T_3$ of the exit water from the mixing point if the ratio of the mass flow rates of the hot to cold water varies from 0.2 to 4 with an increment of 0.2. Plot the outlet temperature as a function of the mass ratio (of hot to cold water). Determine the most suitable mass ratio or range of the mass ratios, provide your justification. Hint: Assume the heat losses from the mixing chamber to be negligible and the mixing to take place at a constant pressure of 250 kPa.

          Problem # 2
Consider an ordinary shower where hot water at $T_1 = 65 \degree C$ is mixed with cold water at $T_2 = 5 \degree C$.
It is desired to steadily supply warm water at $T_3$ for the daily use. Compute the outlet temperature
$T_3$ of the exit water from the mixing point if the ratio of the mass flow rates of the hot to cold water
varies from 0.2 to 4 with an increment of 0.2. Plot the outlet temperature as a function of the mass
ratio (of hot to cold water). Determine the most suitable mass ratio or range of the mass ratios,
provide your justification.
Hint: Assume the heat losses from the mixing chamber to be negligible and the mixing to take
place at a constant pressure of 250 kPa.

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Problem # 2
Consider an ordinary shower where hot water at T1 = 65 C is mixed with cold water at T2 = 5 C.
It is desired to steadily supply warm water at T3 for the daily use. Compute the outlet temperature
T3 of the exit water from the mixing point if the ratio of the mass flow rates of the hot to cold water
varies from 0.2 to 4 with an increment of 0.2. Plot the outlet temperature as a function of the mass
ratio (of hot to cold water). Determine the most suitable mass ratio or range of the mass ratios,
provide your justification.
Hint: Assume the heat losses from the mixing chamber to be negligible and the mixing to take
place at a constant pressure of 250 kPa.

Added by Sara F.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Dominador Tan

01/11/2022

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Step 1: First, we need to determine the outlet temperature T3 of the exit water from the mixing point for different mass flow rate ratios of hot to cold water. Show more…

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i need this part only with details that depend on thermo not only from real-life Determine the most suitable mass ratio or range of the mass ratio Problem #2 Consider an ordinary shower where hot water at T = 65 C is mixed with cold water at T2 = 5 C. It is desired to steadily supply warm water at T3 for the daily use. Compute the outlet temperature T3 of the exit water from the mixing point if the ratio of the mass flow rates of the hot to cold water varies from 0.2 to 4 with an increment of 0.2. Plot the outlet temperature as a function of the mass ratio (of hot to cold water). Determine the most suitable mass ratio or range of the mass ratios provide your justification. Hint: Assume the heat losses from the mixing chamber to be negligible and the mixing to take place at a constant pressure of 250 kPa.

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00:01 For question number one, to identify the pressure of a hot water stream, we need to write first the given.

00:11 For the hot stream temperature, we have t1, which is equals to 80 degrees celsius.

00:18 The hot stream flow rate, which is our m1, is 0 .5 kilogram per seconds.

00:24 The cold stream temperature that is our t2 is 20 degrees celsius.

00:30 The mixture temperature that is our tm is 42 degrees celsius.

00:36 And the cold stream flow, which is the thing that we need to find, is our m2, and the pressure that is 250 kpa.

00:46 For the solution, for the mixture of hot stream and cold stream, the heat supplied by hot stream is equal to heat gain by cold stream.

00:56 So by applying energy balance equation, we get heat supply by hot stream.

01:01 Hot stream.

01:03 So we have qh is equals to m1 cp times t1 minus tm and the heat gain by cold stream is qc is equals to m2 cp times tm minus t2.

01:23 Equating this two we will get m1 cp times t1 t m minus t2 and canceling cp as pressure is constant throughout so we will have m1 t1 minus tm is equals to m2 tm minus t2 so by putting all the value 0 .5 80 minus 42 is equals to m2 42 minus 20 therefore our m2 will be 0 .8636363 per seconds.

02:17 So the cold stream mass flow rate is 0 .863636 kilogram per seconds.

02:26 For question number six, we need to determine the rate of heat transfer in the heat exchanger and the exit temperature of the hot water.

02:37 First is we need to write the give.

02:39 So the mass flow rate of cold water, that is 0 .6 kilograms per seconds...

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