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A large warehouse is 100 m wide, 100 m deep, 10 m high:
a) What is the total weight of the air inside the warehouse?
b) How much pressure does the weight of the air apply on the floor?
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19. Fluid Mechanics
Intro to Pressure
Scelta multipla
The pressure gradient in a pipe carrying water is What pressure gradient would be required to maintain the same flow rate in the same pipe if it were carrying olive oil? Treat the flow as the flow of a viscous fluid. The viscosity of water is and the viscosity of olive oil is .
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B
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There is not enough information to answer the question.
E
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Understand that the flow of a viscous fluid in a pipe is described by Poiseuille's Law, which relates the flow rate to the pressure gradient, the viscosity of the fluid, and the dimensions of the pipe.
Recall Poiseuille's Law: \( Q = \frac{\pi r^4 \Delta P}{8 \eta L} \), where \( Q \) is the flow rate, \( r \) is the radius of the pipe, \( \Delta P \) is the pressure difference, \( \eta \) is the dynamic viscosity, and \( L \) is the length of the pipe.
Since the flow rate \( Q \) and the pipe dimensions \( r \) and \( L \) remain constant, the pressure gradient \( \frac{\Delta P}{L} \) is directly proportional to the viscosity \( \eta \).
Set up the proportionality: \( \frac{\Delta P_{water}}{L} \times \eta_{water} = \frac{\Delta P_{oil}}{L} \times \eta_{oil} \).
Solve for the new pressure gradient for olive oil: \( \frac{\Delta P_{oil}}{L} = \frac{\Delta P_{water}}{L} \times \frac{\eta_{oil}}{\eta_{water}} \). Substitute the given values to find the required pressure gradient for olive oil.
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