A stream of water of density ρ , cross-sectional area A , and speed u strikes a wall that is perpendicular to the direction of the stream, as shown in the figure below. The water then flows sideways across the wall. The force exerted by the stream on the wall is

Question

A stream of water of density ρ , cross-sectional area A , and speed u strikes a wall that is perpendicular to the direction of the stream, as shown in the figure below. The water then flows sideways across the wall. The force exerted by the stream on the wall is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-94lonjf1s879.png" /> (A) ρ u2A (B) ρ u A / 2 (C) 3ρ u2A (D) u2 A / ρ

Tardigrade Admin · Accepted Answer

F=(dp/dt) F=(d (mu)/dt)=(dm/dt)u (dm/dt)=(d/dt)(ÏAx)=ÏA(dx/dt) =ÏAu F=(ÏAu)u F=ÏAu2

Q. A stream of water of density $ρ$ , cross-sectional area $A$ , and speed $u$ strikes a wall that is perpendicular to the direction of the stream, as shown in the figure below. The water then flows sideways across the wall. The force exerted by the stream on the wall is

$ρ u^{2} A$

$ρ u A /2$

$3 ρ u^{2} A$

$u^{2} A / ρ$

$F = \frac{d p}{d t}$
$F = \frac{d ( m u )}{d t} = \frac{d m}{d t} u$
$\frac{d m}{d t} = \frac{d}{d t} (ρ A x) = ρ A \frac{d x}{d t}$
$= ρ A u$
$F = (ρ A u) u$
$F = ρ A u^{2}$

Q. A stream of water of density ρ , cross-sectional area A , and speed u strikes a wall that is perpendicular to the direction of the stream, as shown in the figure below. The water then flows sideways across the wall. The force exerted by the stream on the wall is

ρu2A

ρuA/2

3ρu2A

u2A/ρ