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------------------------------------------------ Fluid is being discharged from a 5 cm diameter nozzle at an average velocity of 5 m/s. If the density of the fluid is 1,000 kg/m\(^3\), what is the mass flow rate of the fluid exiting the nozzle?

A. 0.0982 kg/s
B. 0.982 kg/s
C. 9.82 kg/s
D. 98.2 kg/s
E. 982 kg/s

The mass flow rate of the fluid exiting the nozzle is found using the formula mass flow rate = density * velocity * cross sectional area. After converting units properly, the result is 9.82 kg/s.

Explanation:

The student's question relates to the concept of mass flow rate in fluid dynamics, which is a sub-discipline of physics. The mass flow rate can be calculated using the formula: mass flow rate = density * velocity * cross sectional area. First, we convert the diameter of the nozzle to meters (5 cm = 0.05 m).

The cross sectional area (A) of the nozzle can then be calculated using the formula A=π*(d/2)^2= π*(0.05/2)^2 = 0.00196 m². Substituting the values into the formula, we get: mass flow rate = 1000 kg/m³ * 5 m/s * 0.00196 m² = 9.82 kg/s. Therefore, the mass flow rate of the fluid exiting the nozzle is 9.82 kg/s.

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