An aspirator operates as a pump.Water flows by a small tube perpendicular to the flow of the water.If the water flows at 3.7 m/s,what pressure differential is present if the other end of the tube is maintained at atmospheric pressure?
A)0.93 atm
B)0.69 atm
C)0.31 atm
D)-0.31 atm

Question

Quizplus · Accepted Answer

The pressure differential is given by the Bernoulli equation:$$P_1 + \frac{1}{2} ho v_1^2 = P_2 + \frac{1}{2} ho v_2^2$$where:* $P_1$ is the pressure at the first point* $P_2$ is the pressure at the second point* $ho$ is the density of the fluid* $v_1$ is the velocity of the fluid at the first point* $v_2$ is the velocity of the fluid at the second pointIn this case, $P_2$ is atmospheric pressure, $v_1$ is 3.7 m/s, and $v_2$ is 0 m/s. The density of water is 1000 kg/m^3.Substituting these values into the Bernoulli equation, we get:$$P_1 + \frac{1}{2} (1000 	ext{ kg/m}^3) (3.7 	ext{ m/s})^2 = 101325 	ext{ Pa} + 0$$Solving for $P_1$, we get:$$P_1 = 101325 	ext{ Pa} - 6969 	ext{ Pa} = 94356 	ext{ Pa}$$Converting to atmospheres, we get:$$P_1 = 94356 	ext{ Pa} 	imes \frac{1 	ext{ atm}}{101325 	ext{ Pa}} = 0.93 	ext{ atm}$$Therefore, the pressure differential is 0.93 atm.

An Aspirator Operates as a Pump