Question

Water flows through a tube shown in figure. The area of cross section at A and B are 1 cm2 and 0.5 cm2 respectively. The height difference between A and B is 5 cm. If the speed of water at A is 10 cm s−1 find (a) the speed at B and (b) the difference in pressures at A and B.
Figure

Answer 1

Explanation:

Water flows through a tube shown in figure. The area of cross section at A and B are 1 cm2 and 0.5 cm2 respectively. The height difference between A and B is 5 cm. If the speed of water at A is 10 cm s−1 find (a) the speed at B and (b) the difference in pressures at A and B.

Figure

Water flows through a tube shown in figure. The area of cross section at A and B are 1 cm2 and 0.5 cm2 respectively. The height difference between A and B is 5 cm. If the speed of water at A is 10 cm s−1 find (a) the speed at B and (b) the difference in pressures at A and B.

Figure

Water flows through a tube shown in figure. The area of cross section at A and B are 1 cm2 and 0.5 cm2 respectively. The height difference between A and B is 5 cm. If the speed of water at A is 10 cm s−1 find (a) the speed at B and (b) the difference in pressures at A and B.

FigureWater flows through a tube shown in figure. The area of cross section at A and B are 1 cm2 and 0.5 cm2 respectively. The height difference between A and B is 5 cm. If the speed of water at A is 10 cm s−1 find (a) the speed at B and (b) the difference in pressures at A and B.

FigureWater flows through a tube shown in figure. The area of cross section at A and B are 1 cm2 and 0.5 cm2 respectively. The height difference between A and B is 5 cm. If the speed of water at A is 10 cm s−1 find (a) the speed at B and (b) the difference in pressures at A and B.

FigureWater flows through a tube shown in figure. The area of cross section at A and B are 1 cm2 and 0.5 cm2 respectively. The height difference between A and B is 5 cm. If the speed of water at A is 10 cm s−1 find (a) the speed at B and (b) the difference in pressures at A and B.

FigureWater flows through a tube shown in figure. The area of cross section at A and B are 1 cm2 and 0.5 cm2 respectively. The height difference between A and B is 5 cm. If the speed of water at A is 10 cm s−1 find (a) the speed at B and (b) the difference in pressures at A and B.

Figure

Answer 2

The velocity at B  =20 cm/s

The Bernoulli theorem $=485 N/m^2$

Explanation:

(a) Let level B be the reference for height. Height A

h = 5 cm =0.05 m.  

Vₐ = 10 cm/s =0.10 m/s.  

Cross section field at A =1 cm² = 1/10000m².

So the discharge Q = 0.10 *1/10000m³ =10⁻⁵ m³  

Cross section field at B =0.5 cm² =0.5/10000m²  

The velocity at B = Vᵦ =(10⁻⁵)/(0.5/10000)m/s =  1/5m/s  

=100*1/5cm/s =20 cm/s  

(b) Let Pₐ and Pᵦ.be the stresses at A and B.

The Bernoulli theorem,  

Pₐ+ρgh+1/2 ρVₐ²

= Pᵦ+1/2 ρVᵦ²  Pᵦ -Pₐ  

= ρgh-1/2 ρ(Vᵦ²-Vₐ²)  

=1000*10*0.05 -  1/2*1000*(0.2²-0.1²)  N/m²  

=500 - 500*(0.04-0.01)  N/m²  

=500 - 15 N/m²  

=485 N/m²