00:01
Hello, in the question we have given that oil with viscosity, so the viscosity is given that is equal to 2 into 10 raised to minus 2 newton seconds per meter square and density, so the density of oil is given that is equal to 850 kg per meter cube is pumped along a straight horizontal pipe with a flow rate of 5 decimeter cube per second, so the flow rate is given that is q is equal to 5 decimeter cube divided by seconds per second, so the static pressure difference between two tapping points, so that is 10 meters apart, so the length is given that is 10 meters and the pressure difference is given that is 80 newton per meter square which is nothing but pascals, so assuming laminar flow determine the following things, so first one the pipe diameter and the reynolds number, so from the reynolds number we will again check whether this flow is laminar or not, so first part we are we need to find out the diameter of pipe.
01:34
Now in order to find out the diameter we will use the poiseuille's equation, so poiseuille's equation is given by, so this flow is given by, so this flow is given by pi, so this poiseuille's equation is pi r raised to 4 divided by 8 times viscosity, viscosity we write it as eta but we have called here it as mu, l times the pressure difference that is delta p, so from here if we rearrange for r, so r is the radius, so r will be equal to 8 mu l times q, so this is mu divided by pi delta p, so now and raised to 1 by 4, so now we just have to plug the value and we will get the radius and from radius we can calculate the diameter, so it will be 8 into this is 2 into 10 raised to minus 2 into length is 10 meters times q is 5 decimeter cube, so it will be 5 into 10 raised to minus 3 divided by this 3 .14 into the pressure difference is 80 raised to 1 by 4, so if we calculate, so we will get this r as equal to, so if i calculate this bracketed term, so this will turn out to be 3 .1847 into 10 raised to minus 5 raised to 1 by 4, so from here this r will turn out to be 0 .07512 meters and d the diameter is equals to 2 times of r, so if we calculate we will get this as 0 .07512 times 2, so this d will be equal to 0 .15, so approximately 0 .15 meters, so nearly this.
04:16
So now we have to find out the reynolds number, so in the second part they are asking us to find out the reynolds number.
04:29
Now we have the equation for the reynolds number, so that is r, so i will just write r is equals to rho vd, so where d is the diameter divided by mu the viscosity.
04:47
So now this velocity we need to calculate, so velocity is flow per unit area, so this will be area will be pi d square by 4, so if we calculate this velocity, so let us calculate this, so this is 4 into, so this 4 will go up into q is 5 into 10 raised to minus 3 divided by 3 .14 into 0 .15 square, so from here this velocity will turn out to be 283 .085 into 10 raised to minus 3 meters per second...