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When water drains out of a hole in the bottom of a tank, the stream radius contracts as the speed of the water increases. Assume that the stream starts with zero water velocity at the top of the tank, at a height H above the hole, and ignore all instabilities that will lead to breakup of the stream (turbulence, etc.). Find the distance d beneath the hole at which the radius of the stream is 80% of the hole radius. [Ans: 1.44 H]

When water drains out of a hole in the bottom of a tank, the stream radius contracts as the speed of the water increases. Assume that the stream starts with zero water velocity at the top of the tank, at a height H above the hole, and ignore all instabilities that will lead to breakup of the stream (turbulence, etc.). Find the distance d beneath the hole at which the radius of the stream is 80% of the hole radius. [Ans: 1.44 H]

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Number 2 please and explain how you got the answer Thankyou
### Exercise 1 **Description:** Water flows out of a hole in the side of a large tank at a distance \( h \) below the water surface as shown. The tank is open at the top. **Tasks:** (a) Show that the speed of the water emerging from the hole is \( v^2 = 2gh \). (b) If the water were aimed straight upward coming out of the hole, to what height would it rise? **Diagram Explanation:** A diagram is shown with a large tank filled with water. There is a hole on the side of the tank at a distance \( h \) below the water surface. Water flows out of this hole at velocity \( v \). --- ### Exercise 2 **Description:** When water drains out of a hole in the bottom of a tank, the stream radius contracts as the speed of the water increases. Assume that the stream starts with zero water velocity at the top of the tank, at a height \( H \) above the hole, and ignore all instabilities that will lead to breakup of the stream (turbulence, etc.). **Task:** Find the distance \( d \) beneath the hole at which the radius of the stream is 80% of the hole radius. - **Answer:** \( d = 1.44H \) --- ### Exercise 3 **Description:** A siphon is a device for removing liquid from a container that is not to be tipped. It operates as shown. The tube must be initially filled, but once this has been done the liquid will flow until its level drops below the tube opening at \( A \). The liquid has density \( \rho \) and negligible viscosity. **Diagram Explanation:** The siphon diagram shows a U-shaped tube with points labeled \( A \) and \( B \). The tube is initially filled with liquid, allowing it to siphon the liquid out of the container. These exercises are designed to explore fluid dynamics concepts such as Torricelli's Law and the function of a siphon.
Transcribed Image Text:### Exercise 1 **Description:** Water flows out of a hole in the side of a large tank at a distance \( h \) below the water surface as shown. The tank is open at the top. **Tasks:** (a) Show that the speed of the water emerging from the hole is \( v^2 = 2gh \). (b) If the water were aimed straight upward coming out of the hole, to what height would it rise? **Diagram Explanation:** A diagram is shown with a large tank filled with water. There is a hole on the side of the tank at a distance \( h \) below the water surface. Water flows out of this hole at velocity \( v \). --- ### Exercise 2 **Description:** When water drains out of a hole in the bottom of a tank, the stream radius contracts as the speed of the water increases. Assume that the stream starts with zero water velocity at the top of the tank, at a height \( H \) above the hole, and ignore all instabilities that will lead to breakup of the stream (turbulence, etc.). **Task:** Find the distance \( d \) beneath the hole at which the radius of the stream is 80% of the hole radius. - **Answer:** \( d = 1.44H \) --- ### Exercise 3 **Description:** A siphon is a device for removing liquid from a container that is not to be tipped. It operates as shown. The tube must be initially filled, but once this has been done the liquid will flow until its level drops below the tube opening at \( A \). The liquid has density \( \rho \) and negligible viscosity. **Diagram Explanation:** The siphon diagram shows a U-shaped tube with points labeled \( A \) and \( B \). The tube is initially filled with liquid, allowing it to siphon the liquid out of the container. These exercises are designed to explore fluid dynamics concepts such as Torricelli's Law and the function of a siphon.
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