A fire hose exerts a force on the person holding it. This is because the water accelerates as it goes from the hose through the nozzle. How much force is required to hold a 7.0-cm-diameter hose delivering 420 L$/$min through a 0.75-cm-diameter nozzle?
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in the execution, we have to find the force that is needed to hold the firehouse and we have given the data that is discharge coming out from the knows that which is Q. Z equals two 4 20 later permanent we have given the inside and outside diameter of the nozzle that is given is seven semi, What I can say this is someone to turn to the par -2 m and the two is given to us that is 0.75 semi. Or I can say this can be written as 0.75 to 10 to the power minus two m. This can be literally see uh sorry as a unit so this is 4 20 into one, little is 10 to the Power Ministry meter cube and there is 60 seconds so this will come out to be m two per second so this is 7 to 10 to the Power Ministry meter cubed per second. Now I'm going to show the diagram for the execution so that this is the hose pipe and there is another feature so they let this is our mother and we have given that this is the diameter that is due to this diameter is devon and discharges coming out from this northern so we can see that from continue to equation that is a one way one is equal to a two way too is written that it discharged you is the area of this section that is first section and it was the area of this action that is action to everyone is the velocity of this action that is we won and we do is the velocity of the, what did that is coming out Now we can say that We know that 4th is written as mass into exploration and mars can be written as that is grow into volume and this can be written as exhalation is change rate of change of velocity, dirty tv by delta view by delta T. No, this can for that Britain is that is raw into volume and delta V is changing velocity so this is where two minus we've won upon. This is D Now we can see that this can be written as we buy T. So this is raw into very bitey and this is where two minus we want, we bite is the rate of volume so this can be written as grow into this is cube And from continue to question where you can be written as Q x two and this is Q by Evan or I can say this will be rolled into Q square and this is one upon asia is played by four of the two square minus. This is played by four of The one is square.
Finally we get this can be written as produce where I'm taking four by by common so this is for bye bye into this is one by D two square minus one by devon square. Now put all the data in this equation Through the density of the water, that is 1000 who is the rate of discharge. So this is given to that is 7 to 10 to the Power Monastery meter two per second into four Upon the pie. Outside the area is one upon 0.75 into this is 10 to the power minus two. Holy square minus this is one upon 7 to 10 to the power minus two. All these were. Now I'm going to calculate this. So after holding this part we get, This is forced will be 109, Newton. Or I can say this will be 1100 Newton. So this is the force needed to hold the pipe and this is our answer for the execution. Thank you.