1.

By increasing the volumeof water coming outper secondthe water pumpto n times , what is the powerof motorhas to beincreases ?

Answer»

Solution :Power `P = W/t =(1/2mv^(2))/t`
Where m = mass of WATER coming out from pump .
` :. P =(mv^(2))/(2t)`
` =(Vrhov^(2))/(2t) "" [ :. m = rhoV] `
` :. P = (Alrhot^(2))/(2t) "" [ :. V = Al] `
V = volumeof water coming from the pumpin time t
A = CROSS sectional area of pipe ( is constant )
l = length of FLOW of water
`v = l/t` velocity of water thrown by pump
t = density of water
` :. P = 1/2 A rhov^(2) xx1/t`
` =1/2 Arhov^(3) "" [ :. l/t =v] `
` :. P = 1/2 Arho v^(3)` , here A and `rho `are constant
` :. P prop v^(3) ""....(1)`
` rArr`VOLUME of water coming from cross SECTION of pipe of length l per second
`V = V/t =(Al)/t`
` :. V = Av - to [l/t = v] `
If by increasing the value of V to n times then V = Av (here A is constant )
` :. ` The value of v has to done to n times so from equation (1) ,
` :. ` The value of v has to done t n times so from equation (1) , New power of pump ,
`P prop (nv)^(3)`
` :. P prop n^(3) v^(3)`
` :. P prop n^(3) P `


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