please help me with 6 and 7 with full details.thank you so much Water is flowing

Question

please help me with 6 and 7 with full details.thank you so much

Water is flowing through a copper pipe. The flow is turbulent, and the inner wall of the copper pipe is maintained at 95 degree C. The water enters the pipe at about 5 degree C, and leaves at about 6 degree C. If the flow rate of the water is doubled, will the exit temperature of the water increase, decrease or stay the same? Water is flowing through a brass pipe. The flow is turbulent, and the inner wall of the brass pipe is maintained at 95 degree C. The water enters the pipe at about 5 degree C, and leaves at about 6 degree C. If we put the same number of kg/s of water through a different brass pipe, having half the inner diameter but being in all other respects identical, will the exit temperature of the water increase, decrease or stay the same?

Explanation / Answer

6.

Since for the turbulent flow in a pipe the correlation is given by;

Nu=0.023Re^0.8*Pr

Now if the flow velocity is doubled i.e Re gets doubled since Re is proportional to the flow velocity....

hence nusselt number becomes;

Nu'=1.74 Nu

Since nusselt number increases i.e more heat transfar through convection takes place since nusselt number is proportional to the convection heat transfar and hence final temperature increases............

7.

Since surface area decreases keeping the flow rate same hence final velocity becomes four times.

Now again Re increases by four times,

hence new nusselt number from above correlation,

Nu'=3.03Nu

hence convective heat transfar increases by 3 times but since diameter is halved i.e area decreases by four times

hence finally net heat transfar decreased by approx 25% hence final temperature decreases...

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