A cylindrical metal container 60 cm high, with an inside diameter of 27 cm, weig

Question

A cylindrical metal container 60 cm high, with an inside diameter of 27 cm, weighs 22 N when empty. The container is placed on a scale and water at 20 degree C flows in through an opening in the top and out through two equal-area openings in the sides, as shown in the diagram. Under steady flow conditions, the height of the water in the tank is h = 58 cm. Your boss claims that the scale will read the weight of the volume of water in the tank plus the tank weight, i.e., that we can treat this as a simple statics problem. You disagree, claiming that a flow analysis is required. Who is right, and what is the scale reading in Newtons? A_1 = 95 cm^2 V_1 = -305j cm/s A_2 = A_3 = 43 cm^2

Explanation / Answer

there will be a thrust force in y direction because momentum balance hence scale will read more then just weight of water and tank weight.hence flow analysis is require.

volume of water inside tank= 0.7854d2*h = 0.7854*0.272*0.6=0.03435 m3

weight of water= volume*1000 =0.03435*1000=34.35 kg= 343.5N

Thrust force = m*(v1- v2) = 95/(10000)*1000*0.305*(0.305-0) = 0.884N

TOTAL SCALE READING= 22+343.5+0.884 = 366.384 N

Thanks

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