Answer :
Final answer:
The mass flow rate of water into the tank is 3659.7 lbm/s. In 20 minutes, 1992000 kg of water will flow into the tank. It'll take around 2.28 minutes for 500000 lbm of water to enter the tank.
Explanation:
To compute the mass flow rate, we first need to define flow rate, which is the volume of water flowing through the pipe per unit of time, given in cubic meters per second (m³/s). The volume flow rate (Q) can be found using the formula Q = Area * Velocity, where Area is the cross-sectional area of the pipe (πr²), r is the radius, and Velocity is the speed of the fluid in the pipe.
In this case, given a radius of 18 inches (0.4572 m), and a velocity of 2.5 m/s, we find a flow rate of 1.66 m³/s. We multiply this by the density of water (approximated as 1000 kg/m³) to obtain mass flow rate. Therefore, mass flow rate is 1660 kg/s, or 3659.7 lbm/s.
To determine the mass of water flowing into the tank in 20 minutes, we simply multiply mass flow rate (1660 kg/s) by the time (1200 seconds), which equates to a total of 1992000 kg, or roughly 1992000 kg to the nearest whole number.
Finally, to find out how long it will take for 500000 lbm of water to enter the tank, divide the desired mass by the mass flow rate.
Converting lbm to kg gives approximately 226796 kg, which when divided by the mass flow rate (1660 kg/s) gives approximately 136.6 seconds, or about 2.28 minutes to two decimal places.
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