Water flows steadily through a horizontal pipe of a variable cross-section. If the pressure of the water is p at a point, where the speed of the flow is v, what is the pressure at another point, where the speed of the flow is 2v? Let the density of water be

Options

A. `p+ (3//2) rho v^(2)`
B. `p-2rho v^(2)`
C. `p+2, rho v^(2)`
D. `p-(3//2) rho v^(2)`

Answer

D

Explanation

Two point are situated in a pipe and their height from ground is zero (h=0).
`because` According Bernoulli.s theorem, `p+ rho gh+ (1)/(2) rho V^(2)`= constant
At, a point pressure of water is p and speed of flow is v
therefore, `p+ (1)/(2) rho V^(2)=c` ...(i)
At another point speed of flow is 2v therefore, `p_(1)+ (1)/(2) rho (2v)^(2)= c` ...(ii)
To find pressure `p_(1)` at another point, equation the equation (i) and (ii)
`rArr p+ (1)/(2) rho v^(2)= p_(1) + (1)/(2) rho (4v^(2))`
`rArr p_(1)= p- (3)/(2) rho v^(2)`