00:01
This question we are given here a fresh water jet boat takes a water through a side bend and inject it through a nozzle the diameter we are given here d which is equal to 75 millimeter a millimeter into meter so here we can raise 0 .075 meter now jet speed that is a vr so we are the jet speed so here is the jet speed and the drag for on a board so here we can write the drag force ejecting on a board which is proportional to kumal developed by v where is a v is a board speed and what is the boat speed v is the boat speed now find the expression of the steady speed so here you can wait find the expression of steady speed and the steady speed here is v we want to find the expression here and in terms of water density and flow rate through a cube and also judge speed is v a and vj we are given here that is a vj which is equal to at 15 meter per second so and produce a boat speed bvg is equal to it is 10 meter per second so let's find out the first question in this equation we are given here three force apart in the first subpar of this question we want to find new flow rate so that we want to here we want to find a value of q so how to find value of q here so q which is equal to we know the formula which is equal to a more level where we can write vj now here we just substitute to value into the formulas here you can wait pi d by 4 multiple by d squared multiple we can wait value of vj now we just substitute to value into this formulas here we can write pi divided by 4 value of d is 0 .075 square now we just substitute to value of vj it is 15 now before the simplify and then we get answer here is so answer is 0 .0663 meter cube per second this is the value of flow rate now let's solve our second support of this equation.
02:04
So in this equation, b, so here, in the second support of this question, find a value of quantum k.
02:09
So here, let's find out of the value of constant k.
02:12
So here, how to find value of constant k? we know the following the force, applying the component of the momentum in equation on a control volume drawn.
02:23
So here we can write the force, fh is equal to, here, there is a, we have two forces here, that is a drag force, that one of the one of the first.
02:33
Force that d by d by d and here integration we are given that is cv here that is integration cv and here we can write v that is r d a plus we can write integration of c s that v dv multiplied by we can write and here there's total drag force so here we can write let's find out total drag force which is equal we can write v multiplied by row multiple by q plus we can write that v multiple we can write row multiple by q and here let's substitute value into this formula so here we can write kb square which is equal we can write that v j multiple we can write here row multiple by q minus we can write v multiple we can write r by q now here we just simplify this equation we can write here kb square which is equal to we can write v multiplied by row multiple by q plus we can write v j multiple by we can write here here you can write this is minus here this values minus and here we can write vj and here we can write row by q now here we are solving this equation and then we get answer is so here we can write v which is equal to here we can write minus or minus minus ro multiple q divided by 2k plus we can write square root off here you can write row q divided by 2k and square plus we can write 4k multiple we can write v j multiplied by roe by q divided by we can write here 4 multiplied by k square now let's find out this equation and finding the value of alpha so here alpha which is equal to we can write b squared divided by 2 multiplied by v j minus v how to find value of alpha we just solving this equation and then we get then we get equation is b squared plus 2 multiply by v alpha which is equal we can wait 2 multiply by alpha by vj which is solving this equation then we get value of alpha here now here we are substitute value into this formula so here we can write alpha which is equal to 10 square divided by 2 multiple by vj vj vj is 15 minus 10 now we just simply find we can write your answer is 10 meter per second and this is the value of alpha and we know that alpha which is equal to that is row multiple by q divided by 2 multiple over k now we just simplify and then we get value formula of k k which is equal to we know that that value of row here which is a substitute value of row is 999 the multiple value of q is 0 .0663 divided by 2 multiple value of alpha here is so your value of alpha is 10 now we just simplify and we can write a value is answer here is 3 .3133 3 newton per meter square and newton for meter per second whole square so this is our final answer now let's solve our thoughts are part of this question so in the c so here in this c we want to find the value of v here what is this sphere here board speed and the depth speed is increased by vj which is equal to 25 meter per second so which is speed is increased we want to find value of v here so here we can write value of v which is equal to here we can wait 99 and minus of 999 multiple we can wait 0 .1105 divided by we can write here to multiply by we just substitute all this value into this above formula into this formula and here here we can wait 3 .312 plus we can wait square root off here we can wait square root of that is 999 multiple by here we can weigh 0 .1105 and divided by we can write 2 2 multiply by 3 .312.
06:27
Here you can write that plus whole square and here you can have 4 multiplied by 3 .312 multiply we can write 25 plus we can write 999 multiplied by 0 .1 divided by we can write here 4 multiplied by 3 .312 square.
06:48
Now we just simplify and then we get the answer is the way which is equal to answer here is 6.
06:53
16 .665 meter per second.
06:55
This is the value of v.
06:58
It's fine.
06:58
Last part of this question.
06:59
So in the last part we want to find new flow rate...