A dam on a river is built so that the wall facing the water...

Name: A dam on a river is built so that the wall facing the water is shaped like the region above the curve y = 0.7x^4 and below the line y = 100. (Here, distances are measured in meters.) The water level is 38 meters below the top of the dam. Find the force (in Newtons) exerted on the dam by water pressure. (Water has a density of 1000 kg/m^3, and the acceleration of gravity is 9.8 m/sec^2.)
Uploaded: 2023-02-28T23:15:00-08:00
Duration: 4 min 17 s
Channel: Sri K
Description: A dam on a river is built so that the wall facing the water is shaped like the region above the curve y = 0.7x^4 and below the line y = 100. (Here, distances are measured in meters.) The water level is 38 meters below the top of the dam. Find the force (in Newtons) exerted on the dam by water pressure. (Water has a density of 1000 kg/m^3, and the acceleration of gravity is 9.8 m/sec^2.)

A dam on a river is built so that the wall facing the water is shaped like the region above the curve y = 0.7x^4 and below the line y = 100. (Here, distances are measured in meters.) The water level is 38 meters below the top of the dam. Find the force (in Newtons) exerted on the dam by water pressure. (Water has a density of 1000 kg/m^3, and the acceleration of gravity is 9.8 m/sec^2.)

Transcript

00:01 Hello everyone let's look into this question so there is a dam to water level is in this shape of this curve and the water level is at 60 y is equal to 60 because it is a kind of below on y is equal to 38 meter below that so we have been given the water density and the gravity so we have to find out the force okay so let's first convert y is equal to 0 .7 xx2 power forward into function in y terms so why is equal to 7 by 10 x to the power also x is equal to 10 y by 7 to the power of 1 of 1 4 to the force so this is this is 1 actually but here also will be because we are going to have both sides so this is going to be actually plus and minus so the strip length is this strip length is going to be d x so the strip length is here in this case we are going to have two ten y by seven one upon four okay so let's so the weight of water the weight of water will be given as 9 .8 into the density into 62 minus y the force is given as force will be given us from 0 to 62 this will be given us the weight of the the weight of the water with the area so area will be 2 into 1 7 1 upon 4 device now we will do the integration over over here so after doing the integration that's perform the integration here and we will see what exactly going to be that areas 9 .8 multiplied with 1000 into 2 so we will have 1 960s outside with its constant so 0 to 62 this is going to be 62 minus y and 10 y 117 1 .4 device so we have to do the integral of this so using this integral we will be able to find out the force.

02:48 So for this integral you can use the you can use even calculator.

02:55 So using the calculator we will use the calculator in this case because otherwise it will become very lengthy question so after using the calculator we can see the integral part 1960 so this is going to be so when we the regulation after that we find out 14192 .8974...

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