Question

Consider the barrel shown below. All water here has the same density, which you can take as 1000 kg/m3. Is this barrel emptying, filling, or steady? • If emptying/filling, find the rate. • If steady, find the volume inside. Clearly state assumptions along with your calculations in the uploaded PDF file. You may enter your answer in the textbox, but work must be included in your uploaded file at the end of the exam. 2 Hot Cold water water 210 di v1 d2 V2 d3 3 180 5 200 mm m/s mm m/s mm m/s m kg/m3 v38 D 1.2 P 1000 3

Please solve it step by step. Thanks

Answer 1

Let mass flow rate from different pipes denoted by: m (kg/s)

Mass flow rate in from hot water pipe (kg/s) : m1

m1 = density × cross section area of pipe × velocity

m1 = 1000 ×π d1²/4 × V1

m1 = 1000 × π(0.210)²/4 × 3

m1 = 103.908177 kg/s

Mass flow rate in from cold water pipe : m2

m2 = density × Area × velocity

m2 = 1000 × πd2²/4 × v1

m2 = 1000 × π(0.180)²/4 × 5

m2 = 127.234502 Kg/s

Mass flow rate out from pipe 3 : m3

m3 = density × π× d3²/4 × v3

m3 = 1000 × π(0.200)²/4 × 8

m3 = 251.3274

Total mass flow rate in from pipe 1 and 2 is less than mass flow rate out from pipe 3 , so tank get empty as more water flow out than water flow in.

Rate of emptying tank(m) = m3 - (m1 + m2)

m = 251.3274 - (103.908177 + 127.234502)

m = 20.1847 kg/s

•In steady flow : property of flow does not change with respect to time at any perticular point. flow property remain constant under some assumption .

• pipes are friction less , no loss in pipes

• no effect of datum and pressure head conuted.

• no loss of energy during intermixing of hot and cold fluid.

• tank and exit pipe 3 , has same water temperature .

• height of water inside tank is sufficient to maintain flow condition.

Volume inside tank = area of tank × height of water in tank at that moment

Volume = π× D² / 4 × H

Volume = π× 1.2² /4 ×H

Height data is missing in qustion . Put the value and get volume inside tank.