1.

8. Water is flowing steadily through a horizontal pipeof non-uniform cross-section. At a point, wherethe cross-sectional area of the pipe is 0.02 m2,the pressure of water is 4.0 x 104 N m (or Pa)and its velocity of flow is 2.0 m s. What is theectional area is0.01 m2? The density of water is 103 kg m 3

Answer»

Here we shall first use the continuity equation

av = a'v'

where

a and a' are cross-sectional areas at points 1 and 2 respectively and

v and v' are the velocities of fluid at points 1 and 2 respectively

so,

a =0.02 m^2

v =2 m/s

a' =0.01 m^2

now, as

v' = av / a'

so,

v' = 0.02x2 / 0.01

thus,

v' = 4 m/s

..

now, the Bernoulli's equation is given as (here z = z' - 0)

P/ρ + (1/2)v^2= P'/ρ + (1/2)v'^2

or

P/ρ + (1/2)v^2- (1/2)v'^2= P'/ρ

or

P' = P + (ρ/2)[v^2- v'^2]

now, P = 4 x 10^4N/mm^2= 4 x 10^10N/m^2

and ρ = 1000 kg/m^3

so,

P' = 4 x 10^10+ (1000/2)[2^2- 4^2] ~ 4 x 10^10N/m^2

the answer is close to the initial value


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