Name: Introduction to Fluid Mechanics
Uploaded: 2019-07-19
Duration: 1 min 36 s
Description: A fluid can be at rest like water in a glass or in motion like water flowing in a pipe. This video explains fluid mechanics dealing with the behaviour of the...

Question

On the opposite sides of a wide vertical vessel filled with water two identical holes are opened, each having the cross-sectional area

a = 0.50 {cm}^{2} .

The height difference between them is equal to

h = 51 cm .

Find the resultant force of reaction of the water flowing out of the vessel.

Accepted Answer

Let $A$ and $B$ be two openings, each of area $' a'$ the velocity of water coming out of opening are $V_{A}$ and $V_{B},$ respectively. Volume of water emerging per second through $A$ is $a V_{A} .$ Volume of water emerging per second through $B$ is $a V_{B} .$ Force of reaction due to water coming out at $A$ is given by $F_{A} =$ Rate of change of momentum per second at $A$ $= (a V_{A} ρ) V_{A} = a ρ V_{A}^{2}$

Similarly, the force of reaction at $B$ is given by $F_{B} = a ρ V_{B}^{2}$

Therefore, the net force on the vessel is,

$F = F_{B} - F_{A} = a ρ (V_{B}^{2} - V_{A}^{2}) . . . (i)$

Now, applying Bernoulli's theorem at $A$ and $B,$ we get

$p_{a} + \frac{1}{2} ρ V_{A}^{2} + (h_{2} + h) ρ g = p_{a} + \frac{1}{2} ρ V_{B}^{2} + ρ g h_{2} . . . (ii)$

where $p_{a}$ is atmospheric pressure.

$∴ V_{B}^{2} - V_{A}^{2} = 2 g h$

Substituting this value in Eq. $(i)$ , we get $F = a p 2 g h$

$\Rightarrow F = 2 ρ g a h = 2 \times 1000 \times 10 \times 0.50 \times 10^{- 4} \times 51 \times 10^{- 2}$

$\Rightarrow F = 0.51 N$

On the opposite sides of a wide vertical vessel filled with water two identical holes are opened, each having the cross-sectional area $a = 0.50 {cm}^{2} .$ The height difference between them is equal to $h = 51 cm .$ Find the resultant force of reaction of the water flowing out of the vessel.

Important Questions on Fluid Mechanics

Learn and Prepare for any exam you want !

On the opposite sides of a wide vertical vessel filled with water two identical holes are opened, each having the cross-sectional area a=0.50 cm2. The height difference between them is equal to h=51 cm. Find the resultant force of reaction of the water flowing out of the vessel.

Important Questions on Fluid Mechanics

Learn and Prepare for any exam you want !

On the opposite sides of a wide vertical vessel filled with water two identical holes are opened, each having the cross-sectional area $a = 0.50 {cm}^{2} .$ The height difference between them is equal to $h = 51 cm .$ Find the resultant force of reaction of the water flowing out of the vessel.