{"id":2236,"date":"2018-04-29T03:06:54","date_gmt":"2018-04-28T19:06:54","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=2236"},"modified":"2023-08-08T14:09:02","modified_gmt":"2023-08-08T14:09:02","slug":"torricellis-theorem-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/torricellis-theorem-problems-and-solutions.htm","title":{"rendered":"Torricelli’s theorem \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

Torricelli’s theorem \u2013 problems and solutions<\/span><\/p>\n

1. A tube with the height of 100 cm filled with water. A hole Q located at 10 cm above the ground. What is the horizontal distance (x)?<\/span><\/p>\n

Known :\"Torricelli's<\/u><\/span><\/p>\n

Distance between hole and the surface of the water (h) = 100 cm \u2013 10 cm = 90 cm = 0.9 m <\/span><\/p>\n

Acceleration due to gravity<\/a> (g) = 10 m\/s2<\/sup><\/span><\/p>\n

Wanted:<\/u> Distance of x<\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

The speed of the water flow at the hole <\/b><\/span><\/p>\n

\"Torricelli's<\/span><\/p>\n

v = <\/i>speed<\/i>, g = <\/i>acceleration due to gravity<\/i>, h = <\/i>distance between the hole and the surface of the water<\/i><\/span><\/p>\n

The speed of the water flow at the hole :<\/span><\/p>\n

\"Torricelli's<\/span><\/p>\n

Time in air<\/b><\/span><\/p>\n

\"Torricelli'sThe motion of water from the hole to the ground is the projectile motion<\/a>. The projectile motion could be understood by analyzing the horizontal and vertical component of the motion separately. The x motion occurs at a constant velocity and the y motion occurs at a constant acceleration of gravity. <\/span><\/p>\n

In this problem, vertical motion<\/a> analyzed as free fall motion.<\/span><\/p>\n

Calculate time in air using the equation of the free fall motion<\/a>. <\/span><\/p>\n

Known :<\/u><\/span><\/p>\n

The height of hole (y) = 10 cm = 0.1 m<\/span><\/p>\n

Acceleration due to gravity (g) = 10 m\/s2<\/sup><\/span><\/p>\n

Wanted :<\/u> Time interval (t)<\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

y = 1\/2 g t2<\/sup><\/span><\/p>\n

0.1 = 1\/2 (10) t2<\/sup><\/span><\/p>\n

0.1 = 5 t2<\/sup><\/span><\/p>\n

t2 <\/sup>= 0.1 \/ 5<\/span><\/p>\n

t2 <\/sup>= 0.02<\/span><\/p>\n

t = \u221a0.02 seconds<\/span><\/p>\n

The horizontal distance (x) :<\/b><\/span><\/p>\n

Known :<\/u><\/span><\/p>\n

The initial velocity (vo<\/sub> = vox<\/sub>) = 3\u221a2 m\/s<\/span><\/p>\n

Time in air (t)= \u221a0.02 seconds<\/span><\/p>\n

Wanted : <\/u>The horizontal distance (x)<\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

v = x \/ t<\/span><\/p>\n

x = v t = (3\u221a2)(\u221a0.02) = (3)(1.41)(0.14) = 0.59 = 0.6 meters<\/span><\/p>\n

2. A tank containing water with height of 1 meter. At point P, there is a hole. What is the speed of water flow at the hole. Acceleration due to gravity is 10 m\/s2<\/sup>.<\/span><\/p>\n

Known :<\/u><\/span><\/p>\n

Distance between hole and the surface of the water (h) = 100 cm \u2013 80 cm = 20 cm = 0.2 m \"Torricelli's<\/span><\/p>\n

Acceleration due to gravity (g) = 10 m\/s2<\/sup><\/span><\/p>\n

Wanted:<\/u> Speed of the water flow at the hole (v)<\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

The speed of the water flow at the hole :<\/span><\/p>\n

\"Torricelli's3. A larg<\/span>e tub <\/span>contains water and there is a faucet as shown in the picture below. If g = 10 ms<\/span>-2<\/span><\/sup>, then the water velocity out of the faucet is…<\/span><\/span><\/p>\n

Known :\"Teorema<\/u><\/span><\/p>\n

Height (h) = 85 cm \u2013 40 cm = 45 cm = 0.45 meters<\/span><\/p>\n

Acceleration due to gravity (g) = 10 m\/s2<\/sup><\/span><\/p>\n

Wanted:<\/u> Speed of water (v)<\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

T<\/a>orricelli’s theorem states that the velocity of water through a hole distant h from the surface of water equals the <\/span>speed of <\/span>free fall<\/span>ing <\/span>water from a height of h.<\/span><\/span><\/p>\n

Water velocity is calculated using the free fall motion formul<\/span>a <\/span>v<\/i>t<\/i><\/sub>2<\/i><\/sup> = 2 g h<\/i> <\/span><\/p>\n

vt<\/sub>2<\/sup> = 2 g h = 2(10)(0.45) = 9<\/span><\/p>\n

vt<\/sub> = \u221a9 = 3 m\/s <\/span><\/p>\n

4. A <\/span>tub <\/span>filled with water and on a wall there is a hole (see <\/span>figure below<\/span>). The speed of water coming out of the hole is\u2026 <\/span>(g = 10 ms-2<\/sup>)<\/span><\/p>\n

Known :\"Teorema<\/u><\/span><\/p>\n

Height (h) = 1.5 m \u2013 0.25 m = 1.25 meters<\/span><\/p>\n

Acceleration due to gravity (g) = 10 m\/s2<\/sup><\/span><\/p>\n

Wanted :<\/u> Speed of water <\/span>(v)<\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

vt<\/sub>2<\/sup> = 2 g h = 2(10)(1.25) = 25<\/span><\/p>\n

vt<\/sub> = \u221a25 = 5 m\/s <\/span><\/p>\n

5. A tank containing water as high as 1 meter (g = 10 ms<\/span>-2<\/span><\/sup>) and on the wall there is a leak hole (see <\/span>figure below<\/span>). The speed of water coming out of the hole is …<\/span><\/span><\/p>\n

Known :<\/u><\/span><\/p>\n

Height (h) = 1 m \u2013 0.20 m = 0.8 meters\"Teorema<\/span><\/p>\n

Acceleration due to gravity (g) = 10 m\/s2<\/sup><\/span><\/p>\n

Wanted :<\/u> Speed of water <\/span>(v)<\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

vt<\/sub>2<\/sup> = 2 g h = 2(10)(0.8) = 16<\/span><\/p>\n

vt<\/sub> = \u221a16 = 4 m\/s <\/span><\/p>\n

    \n
  1. What does Torricelli’s theorem describe?<\/strong><\/span>\n