WE have a Pressure Gauge and we want to measure static and total pressure of a particular flow through a pipe. How can we measure that.
If we want to measure just the static pressure inside the pipe and we need to place pressure gauge tangential to the flow of the liquid inside the pipe. If we want to measure the complete head of the flow, we should place the inlet of pressure gauge against the direction of flow. That way, with application of Bernaulli's equation, we can get the total head as (P + dgh +0.5 dv^2). Remember the assumptions while applying the equation: Flow is inviscid, You can apply the equation only along the streamline of the flow ( read up on stream line and streak line of a flow). You ignore the boundary disturbances in that.
Differentiate (x^2 +x)^2
Let's approach this sum step by step. In the end you should be able to get the answer in single step. :) consider (x^2 +x)^2 as t so 1st differentiate t^2, which is 2t = 2(x^2 +x) now get one step inside the bracket. that is x^2+x and differentiate this, that is 2x+1 In the end keep on multiplying the results whenever you go one step inside the bracket. Hence the answer is : 2(x^2 +x)* (2x+1)
There are 5 different cold drinks, 3 different burgers, 2 different soups in a restaurant where you have come to eat. In how many ways can you select at least one from each?
When you consider an object, you can act in 2 ways. Either you select it or reject it. So in case of cold drinks, you can act in 2 ways for each of them. therefore there are 2^5 -1 possibilities of selection. I subtracted 1 because there is one case in which you wont be selecting any drink. Perform similar steps in the other two. The answer is : (2^5 -1) * (2^3 -1)*(2^2 -1) Note: We had to select at least 1 object from each category hence we subtracted one from each category .