A large storage tank, open to the atmosphere at the top and fi lled with water, develops a small hole in its side at a point 16.0 m below the water level. If the rate of fl ow from the leak is 2.50 103 m3 /min, determine (a) the speed at which the water leaves the hole and (b) the diameter of the hole

The speed at which the water leaves the hole = 4.21

The value of  diameter of the hole d = 0.112 m = 11.2 cm

Step-by-step explanation:

Given data

Flow rate = 2.5 × = 0.0416 ×

Height (h) = 16 m

(a) The speed at which the water leaves the hole :-

Apply bernouli equation for the water tank at point 1 & 2

------ (1)

Since = , &

Equation (1) becomes

=

This is the speed at which the water leaves the hole.

Put the values of g & h in the above formula

⇒ 2 g h = 2 × 9.81 × 16 = 17.71

= =

= 4.21

This is the speed at which the water leaves the hole.  

(b)Diameter of the hole :-

We know that flow rate Q = A × V

Put the values of Q & V in the above formula we get

A =   ×

A = 9.88 ×

We know that area A =

⇒ = × 9.88 ×

⇒ = 0.01258

⇒ d = 0.112 m = 11.2 cm

this is the value of  diameter of the hole.

c

step-by-step explanation:

the height of the surface increases from the center out to the sides of the road.

step-by-step explanation:

as we move out we move away from the x-axis.

and as mentioned in the problem statement that height of a road increases when we move away from the center x.

hence proved that 3rd option

the height of the surface increases from the center out to the sides of the road.

is the correct option.