By what factor is the total pressure greater at a depth of 650 m in water than at the surface where the pressure is one atmosphere? (water density = 1.0 × 10³ kg/m³,1 atmosphere pressure = 1.01 × 10⁵ N/m²,and g = 9.8 m/s²) A) 100 B) 83 C) 64 D) 19

Question

Quizplus · Accepted Answer

The pressure at a depth of 650 m in water can be calculated using the formula:

P = P0 + ρgh

where P0 is the pressure at the surface (1 atmosphere), ρ is the density of water, g is the acceleration due to gravity, and h is the depth.

Plugging in the values, we get:

P = 1.01 × 10^5 Pa + (1.0 × 10^3 kg/m^3) × (9.8 m/s^2) × (650 m) 
  = 6.368 × 10^6 Pa

The factor by which this pressure is greater than the pressure at the surface (1 atmosphere = 1.01 × 10^5 Pa) is:

6.368 × 10^6 Pa ÷ 1.01 × 10^5 Pa ≈ 63.0

Rounding to the nearest whole number, we get:

63 ≈ 64

Therefore, the total pressure at a depth of 650 m in water is about 64 times greater than at the surface, or choice C.

By What Factor Is the Total Pressure Greater at a Depth