Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 1044

A tank is filled with water up to a height \(\mathrm{H}\). Water is allowed to come out of a hole P in one of the walls at a depth \(\mathrm{D}\) below the surface of water express the horizontal distance \(\mathrm{x}\) in terms of \(\mathrm{H}\) and \(\mathrm{D}\). (B) $\left.\mathrm{x}={ }^{\alpha} \sqrt{[}\\{\mathrm{D}(\mathrm{H}-\mathrm{D})\\} / 2\right]$ (D) \(\mathrm{x}=4[\mathrm{D}(\mathrm{H}-\mathrm{D})]\)

Short Answer

Expert verified
The short answer is: \(x = \sqrt{4D(H - D)}\).

Step by step solution

01

Find the Initial Vertical Velocity

To calculate the initial velocity of the water as it leaves the hole, we can use Torricelli's theorem, which states that the speed of the fluid at the hole is equal to the speed it would acquire if it fell freely from a height equal to the depth of the hole. Therefore, the velocity of the water, v, can be found using the equation: \(v = \sqrt{2gD}\), where g is the acceleration due to gravity (approximately 9.81 m/s^2).
02

Calculate Time to Hit the Ground

As the water leaves the hole horizontally with velocity v, it will also be subject to gravity, which will make it fall towards the ground. We can use kinematic equations to find the time it takes for the water to reach the ground. In this case, we have the following equation: \((H - D) = \frac{1}{2}gt^2\), where t is the time it takes for the water to hit the ground. We need to solve this equation for t: \(t = \sqrt{\frac{2(H - D)}{g}}\).
03

Calculate the Horizontal Distance x

Now that we have the initial horizontal velocity of the water and the time it takes to reach the ground, we can calculate the horizontal distance x: \(x = vt\), where x is the horizontal distance, v is the horizontal velocity, and t is the time found in step 2. Substitute the values for v and t from steps 1 and 2: \(x = \sqrt{2gD} \cdot \sqrt{\frac{2(H - D)}{g}}\), \(x = \sqrt{2gD \cdot \frac{2(H - D)}{g}}\). Simplifying the expression, we get: \(x = \sqrt{4D(H - D)}\). The correct answer is (D) \(x=4[D(H-D)]\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Mercury thermometers can be used to measure temperatures up to (A) \(100^{\circ} \mathrm{C}\) (B) \(212^{\circ} \mathrm{C}\) (C) \(360^{\circ} \mathrm{C}\) (D) \(500^{\circ} \mathrm{C}\)

The poisson's ratio cannot have the value.......... (A) \(0.7\) (B) \(0.2\) (C) \(0.1\) (D) \(0.5\)

A large number of water drops each of radius \(r\) combine to have a drop of radius \(\mathrm{R}\). If the surface tension is \(\mathrm{T}\) and the mechanical equivalent at heat is \(\mathrm{J}\) then the rise in temperature will be (A) \((2 \mathrm{~T} / \mathrm{rJ})\) (B) \((3 \mathrm{~T} / \mathrm{RJ})\) (C) \((3 \mathrm{~T} / \mathrm{J})\\{(1 / \mathrm{r})-(1 / \mathrm{R})\\}\) (D) \((2 \mathrm{~T} / \mathrm{J})\\{(1 / \mathrm{r})-(1 / \mathrm{R})\\}\)

The bulk modulus of an ideal gas at constant temperature..... (A) is equal to its volume \(\mathrm{V}\) (B) is equal to \(\mathrm{P} / 2\) (C) is equal to its pressure \(\mathrm{P}\) (D) cannot be determined

A material has poisson's ratio \(0.50\). If uniform rod of it suffers longitudinal strain of \(2 \times 10^{-3}\). Then what is percentage change in volume ? (A) \(0.6\) (B) \(0.4\) (C) \(0.2\) (D) 0
See all solutions

Recommended explanations on English Textbooks

Linguistic Terms

Read Explanation

History of English Language

Read Explanation

Prosody

Read Explanation

Lexis and Semantics Summary

Read Explanation

Language and Social Groups

Read Explanation

Research and Composition

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free