 Okay, this is a problem where we are trying to calculate volumetric flow rate through Alaskan pipeline. The pipeline is four and a half feet in diameter and the length of the pipeline is 800 miles and the velocity with which the oil is flowing through that crude oil is is 6.0 feet per second and what we are up to is to calculate how many barrels of oil are flowing through and what is the volumetric flow rate and also the mass how much mass because the Oil is flowing through the through the pipeline. It acts like a storage bin for us So let's calculate first the volumetric flow rate volumetric flow rate is Is calculated by knowing the area of the pipe and we know the length of the pipe is 800 miles. So area of the pipe or cross-sectional area would be Pi r square or pi over 4d square since diameter is given we could use that pi over 4 times d diameter is 4.5 feet now Square that will give us the area now area times length would give us the volume volume is now Pi over 4 times 4.5 feet square All right times The length that we have is 800 miles So this is in feet square or Feet length and this is in miles. So we need to convert these miles into feet again. So one mile is equal to 5,280 feet So now we have miles and miles gone. So we will have Everything in feet. So the answer will be in cubic feet So that will be the volume and The velocity with which It is going through is six feet per second. So we can calculate the Volumetric flow rate actually So volume of the pipe is this but the rate at which it is flowing will be six feet per second So let's calculate the volume of the pipe actually how much we can store in here So this is coming out to be 671 457 600 feet cube All right, this is the wall gym if the Velocity is six feet per second or let's calculate the barrels of oil that we can store here But immediately now with this barrels of oil that would be more logical here. So the conversion factor is one feet cube equal to Point two three 74 barrels Actually one barrel is 42 US gallons and we can convert to First gallons and then gallons to cubic feet also in a conversion factor But straight away one cubic foot is equal to point two three seven four barrels So now if we were to convert this To barrels now one feet cube equal to point two three seven four This is barrels So now the answer would be in barrels So that would be so this will be one hundred and fifty nine Four hundred and four zero three four so we are talking about One hundred and fifty nine Million barrels 159.4 million barrels of oil that we're talking about here That can be stored. So that is a large volume that we can store in the pipelines So similarly for natural gas also we have a lot of storage capacity in this country We have a million miles of pipeline at 64 bar or atmospheres pressure The gas is transmitted throughout the United States So which means basically underground storage or transport can provide a lot of storage area Now let's get back to this calculation of Mass flow rate if we know the volumetric flow rate we can calculate the mass flow rate So what for volumetric flow rate? We need we have the area volumetric flow rate now. This is the volume that we calculated volumetric flow rate Is we have the area and how much is passing through this cross-sectional area? so this is the area of The pipeline and every second six feet is passing by okay So the volumetric flow rate would be a divided by four 4.5 Square this is the area times Velocity would be six feet per second so every second This much oil is passing through which is basically 95 0.3 Feet cube this is feet square Times feet here feet cube per second So every second 95.3 feet cube of oil is flowing through So per hour if we calculate it would be times 3600 there are three thousand six hundred seconds in an hour, so That would be so every hour we are talking about 343,359 Feet cube of oil per hour Okay, so we can we can go on to do the calculation in a year how much we can we can transport by multiplying this by if 24 hours of flow per day and Then there are three hundred and sixty-five days There are three hundred and sixty-five days so Days and days and hours and hour get cancelled so you know how much oil is going out per year So that would be Believe it or not that value comes out to be 3.0 Times ten raised to nine roughly this is feet cube three billion cubic feet of oil is flowing through So if we were to this is per year if we do the same calculation as how many barrels are flowing through We can multiply this by point zero Point two three seven four like we did before. This is the barrels to feet cube conversion So feet cube and feet cube get cancelled how many barrels of oil are we transporting through this per year? We're talking about here 714 Million barrels per year. So that is the flow rate. All right, so that gives us the volumetric flow rate mass flow rate is this times density Okay Volume times density. Let me erase this here okay now Specific gravity is density of a medium divided by the density of water so Specific gravity is given to us specific gravity is given as point eight six and Specific gravity is actually Row of oil specific gravity of oil here row of the medium divided by row of water Okay, so Since we know the row of water which happens to be sixty two point four pounds per cubic foot and Row of oil can be calculated because we know the fraction. This is point eight six So in this case a row of oil would be point eight six times sixty two point four This will give us pounds per cubic feet and we also know that There is the total Or mass flow can be calculated by as close mass flow is volumetric flow Times density volumetric flow is calculated as three billion feet cube per year Times density is Point eight six times sixty two point four pounds per feet cube So feet cube feet cube can be cancelled. So now we know the mass flow what we are getting This is coming out to be Three point eight three times ten raised to ten This would be Pounds per year. So this is the mass flow of the oil. This is a lot of mass. We're talking about Flowing through the Alaskan pipeline. That's it