Question

A body moving through still water at 8 m/s produces a water velocity of 5 m/sec at a point 1 m ahead. The difference in pressure between the nose and the point 1 m ahead would be

• A. $4500N/m^2$
• B. $6000N/m^2$
• C. $19500N/m^2$
• D. $12000N/m^2$

Answer 1

The correct option is A $4500N/m^2$

Velocity at Nose $=8m/s$

Velocity at 1 m ahead $=5m/s$

Let pressure at Nose and 1 m ahead are $p_1$ and $p_2$ respectively.

From Bernoulli's equation (in terms of relative velocity)
$\frac{p_1}{\rho g}+Z_1+\frac{V_1^2}{2g}=\frac{p_2}{\rho g}+Z_2+\frac{V_2^2}{2g}$

$\frac{p_2-p_1}{\rho g}=\frac{(3{)}^2-(0{)}^2}{2g}$

(Relative velocity of point 1 with respect to 2 is $8-5=3m/s$)

$p_2-p_1=4500N/m^2$