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The figure shows the commonly observed d...

The figure shows the commonly observed decrease in diameter of a water stream as it falls from a tap. The tap has internal diameter `D_(0)` and is connected toa large tank of water. The surface of the water is at a height `b` above the end of the tap.
By considering the dynamics of a thin "cylinder" of water in the steam answer the following: (ignore any reistance to the flow and any effects of surface tansion, given `rho_(w) =` density of water)

Equation for the flow rate, i.e. the mass of water flowing through a given point in the stream per unit time, as funcation of the water speed `v` will be

A

`vrho_(w)piD^(2)//4`

B

`vrho_(w)(piD^(2)//4 - piD_(0)^(2)//4)`

C

`vrho_(w)piD^(2)2`

D

`vrho_(w)piD_(0^(2))//4`

Text Solution

Verified by Experts

The correct Answer is:
A
`(A)` As, `dm = Arhom vdt`
`rArr (dm)/(dt) = Arhow^(v) rArr (dm)/(dt) = Vrho_(W)pi (D^(2))/(4)` where `'D'` is the diameter of stream.
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Knowledge Check

  • The figure shows the commonly observed decrease in diameter of a water stream as it falls from a tap. The tap has internal diameter D_(0) and is connected toa large tank of water. The surface of the water is at a height b above the end of the tap. By considering the dynamics of a thin "cylinder" of water in the steam answer the following: (ignore any reistance to the flow and any effects of surface tansion, given rho_(w) = density of water) Equation for the stream diameter D in terms of x and D_(0) will be :

    A
    `D = D_(0)((b)/(b + x))^(1//4)`
    B
    `D = D_(0)((b)/(b + x))^(1//2)`
    C
    `D = D_(0)((b)/(b + x))`
    D
    `D = D_(0)((b)/(b + x))^(2)`

  • The figure shows the commonly observed decrease in diameter of a water stream as it falls from a tap. The tap has internal diameter D_(0) and is connected toa large tank of water. The surface of the water is at a height b above the end of the tap. By considering the dynamics of a thin "cylinder" of water in the steam answer the following: (ignore any reistance to the flow and any effects of surface tansion, given rho_(w) = density of water) The equation for the water speed v as a funcation of the distance x below the tap will be:

    A
    `v = sqrt(2gb)`
    B
    `v = [2g (b + x)]^(1//2)`
    C
    `v = sqrt(2gx)`
    D
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  • The figure shows the commonly observed decrease in diameter of a water stream as it falls from a tap. The tap has internal diameter D_(0) and is connected toa large tank of water. The surface of the water is at a height b above the end of the tap. By considering the dynamics of a thin "cylinder" of water in the steam answer the following: (ignore any reistance to the flow and any effects of surface tansion, given rho_(w) = density of water) Which of the following equation expresses the fact that the flow rate at the tap is the same as at the stream point with diameter D and velocity v (i.e. D in terms of D_(0), v_(0) and v will be) :

    A
    `D = (D_(0)v_(0))/(v)`
    B
    `D = (D_(0)v_(0)^(2))/(v^(2))`
    C
    `D = (D_(0)v)/(v_(0))`
    D
    `D = D_(0)sqrt((v_(0))/(v))`

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