A pump uses a piston of 15 cm diameter which moves 2 cm/s. What is the fluid velocity of a tube 3 cm in diameter?

Question

BlackTom AI · Accepted Answer

We start by identifying the principle: conservation of volumetric flow rate in an incompressible fluid means Q = A1 * v1 = A2 * v2.
Option 1 examines the piston side: the piston has a diameter of 15 cm, so its radius is 7.5 cm. The cross-sectional area is A1 = π(0.075 m)^2 ≈ 0.01767 m^2. The piston velocity is 2 cm/s = 0.02 m/s, so the flow rate is Q = A1 * v1 ≈ 0.01767 * 0.02 ≈ 0.000353 m^3/s.
Option 2 looks at the tube side: the tube diameter is 3 cm, so radius 1.5 cm. The cross-sectional area is A2 = π(0.015 m)^2 ≈ 0.0007069 m^2.
To find the fluid velocity in the tube, v2 = Q / A2 ≈ 0.000353 / 0.0007069 ≈ 0.5 m/s, which is 50 cm/s.
Option 3 proposes 6 cm/s. If we test this, the implied Q would be A2 * v2 = 0.0007069 m^2 * 0.06 m/s ≈ 0.0000424 m^3/s, which is far smaller than the piston’s Q ≈ 0.000353 m^3/s, indicating inconsistency with flow continuity.
Option 4 suggests 50 m/s. Converting, that would require Q = A2 * v2 = 0.0007069 m^2 * 50 m/s ≈ 0.0353 m^3/s, which is about 100 times larger than what the piston can supply, making this physically impossible in this system.
In summary, only the velocity that satisfies Q = A1*v1 on the piston side and Q = A2*v2 on the tube side is v2 ≈ 0.5 m/s (50 cm/s). The given calculations align with conservation of mass for an incompressible fluid, and the other options fail either due to dimensional mismatch or by violating the continuity of flow.

A pump uses a piston of 15 cm diameter which moves 2 cm/s. What is the fluid velocity of a tube 3 cm in diameter? 单项选择题

类似问题

A cylindrical tank has diameter D=1.20 m. It starts at h0=0.30 m and must reach h=0.80 m. The inlet volumetric flow rate is Qin=0.0026 m^3/s and the outlet volumetric flow rate is Qout=0.0009 m^3/s. Find the time required.

An ideal fluid flows through a horizontal pipe made of two sections with diameters of 1.0 and 2.0 cm, respectively. The speed of the fluid flow through the 2.0-cm section will be what factor times that through the 1.0-cm section?

A river 935 m wide and 3.5 m deep, flowing at 1.5 m sec-1 enters narrow canyon 55 m wide and 15 m deep. What is the average river speed in the canyon assuming its cross section is a elliptical? The area of an ellipse is 𝜋 a b, where a and b are the two axes of the ellipse.

Consider volume V with incoming and outgoing flows. The fluid cannot be considered incompressible. Which of the following variations of continuity equation can be used to describe the situation?

What was the world's first widely adopted biodiversity policy?

The aim of the Paris Agreement is to ensure that the earth’s preindustrial temperature is not exceeded by more than º Celsius.

The IPCC's mission is to Blank ______.

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单