At what speed, the velocity head of the water is twice than that of pressure head of 75 cm of Hg ?

Question

At what speed, the velocity head of the water is twice than that of pressure head of 75 cm of Hg ? (A) 10 m / s (B) 20 m / s (C) 30 m / s (D) 40 m / s

Tardigrade Admin · Accepted Answer

Pressure head =( P /ρ g ) ; velocity head =( V 2/2 g ) (V2/2 g)=(2 P/ρ g) ⇒ V2=(4 P/ρ) V 2=(4 × 75 × 10-2 × 13.6 × 103 × 9.8/103) =39984 × 10-2=399 V ≈ 20 m / s

Q. At what speed, the velocity head of the water is twice than that of pressure head of $75 c m$ of $H g$ ?

$10 m / s$

$20 m / s$

$30 m / s$

$40 m / s$

Pressure head $= \frac{P}{ρ g};$
velocity head $= \frac{V ^{2}}{2 g}$
$\frac{V ^{2}}{2 g} = \frac{2 P}{ρ g}$
$\Rightarrow V^{2} = \frac{4 P}{ρ}$
$V^{2} = \frac{4 \times 75 \times 1 0 ^{- 2} \times 13.6 \times 1 0 ^{3} \times 9.8}{1 0 ^{3}}$
$= 39984 \times 1 0^{- 2} = 399$
$V \approx 20 m / s$

Q. At what speed, the velocity head of the water is twice than that of pressure head of 75cm of Hg ?

10m/s

20m/s

30m/s

40m/s