A small circular hole 6.00 mm in diameter is cut in the side of a large water tank. The top of the tank is open to the air. The water is escaping from the hole at a speed of 10 m/s. How far below the water surface is the hole

The water surface is 5.10 m below the hole.

Given data:

The diameter of circular hole is, d = 6.00 mm = 0.006 m.

The speed of water escaping through hole is, v = 10 m/s.

Here, we will apply the concept of kinematic equation of motion. As per the third kinematic equation of motion,

here,

u is the initial speed of water.

g is the gravitational acceleration.

h is the vertical distance of hole from the water surface..

Solving as,

Thus, we can conclude that the water surface is 5.10 m below the hole.

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5.097 m

Explanation:

This involves Bernoulli's equation, so we will use;

P + ρgh + ½ρv² = constant

Applying this equation to both points, we have;

P_i + ρ_water*g*h_i + ½*ρ_water*v_i² = P_f + ρ_water*g*h_f + ½*ρ_water*v_f²

Since open to air, P_i and P_f will cancel out.

Also, v_i = 0 and h_f = 0

ρ_water = 1 g/ml

v_f is given as 10 m/s

h_i is depth of the hole below the water surface.

Thus, plugging in values, we have;

1*9.81*h_i + 0 = 0 + ½*1*10²

9.81h_i = 50

h_i = 50/9.81

h_i = 5.097 m

freezing

deposition

condensation

explanation;

melting also called fusion is the process where solid becomes liquid, sublimation is the process where solid becomes gaseous without first changing to liquid, deposition involves change from gaseous to solid state, freezing involves change from liquid to solid, boiling or evaporation involves change of liquid to gaseous state, while condensation is the change from gaseous state to liquid state.

endothermic reactions involves absorption of heat from the surroundings or the environment while exothermic reactions involves loss of heat energy to the surroundings.

in this case, sublimation, evaporation and melting are endothermic reactions (gain energy from the environment) while, freezing, deposition and condensation are exothermic (loss of energy to the surroundings) reactions.