Re: [OT] Wasserstoff (Handelsblatt)

From	Carla Schneider <carla_schn@proton.me>
Newsgroups	de.sci.electronics
Subject	Re: [OT] Wasserstoff (Handelsblatt)
Date	2024-05-29 08:41 +0200
Organization	Mausgrau
Message-ID	<6656CE0C.C0D9D391@proton.me> (permalink)
References	(10 earlier) <v31bmn$3tp3b$2@dont-email.me> <66547794.340DA172@proton.me> <20240527220028.1043d105@Achmuehle.WOR> <6655B17A.F82C9705@proton.me> <20240528211727.1d885f22@Achmuehle.WOR>

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Sieghard Schicktanz wrote:
> 
> Hallo Carla,
> 
> Du schriebst am Tue, 28 May 2024 12:27:06 +0200:
> 
> > > > immer gleich viel Material pro Kubikmeter Speicherplatz verbraucht
> ...
> > > > Chatgpt zeigt die Formel...
> > >
> > > ZEIGEN!
> 
> > Die Formeln kann ich wegen des Zeichensatzes hier nicht hineinposten,
> > aber der Chat ist hier zu sehen:
> 
> Faule Ausrede. Und: _deswegen_ tu' ich mir dieses Zeugs nicht an!

Sicher nicht deswegen, die Formel in Schoenschriftist ein Service fuer
den Benutzer, selbstverstaendlich kann Chatgpt auch eine Ausgabe in 
ASCII, die sieht natuerlich nicht so gut aus:


------------------
ChatGPT
How much steel is required for a hollow sphere  that has to withstand a given pressure from the
outside,
I want a formula that gives me the  Mass of Steel dependent on the inner radius of the sphere.

ChatGPT
To determine the mass of steel required for a hollow sphere that has to withstand a given external
pressure, we'll use the principles of pressure vessel design. Here's a step-by-step approach to
derive the formula:

### Step 1: Understand the Parameters
Let's define the parameters:
- \( P \): External pressure
- \( r_i \): Inner radius of the sphere
- \( t \): Thickness of the sphere's wall
- \( \sigma \): Allowable stress for the steel
- \( \rho \): Density of steel

### Step 2: Formula for Wall Thickness
For a thin-walled sphere subjected to external pressure, the wall thickness \( t \) can be
approximated using the following formula derived from the hoop stress equation:
\[ t = \frac{P r_i}{2\sigma} \]

For thick-walled spheres, the Lamé's equations are used, but let's start with the thin-walled
approximation. If needed, adjustments can be made for thicker walls.

### Step 3: Volume of Steel
The volume of the steel shell \( V \) can be approximated by the volume difference between the outer
sphere and the inner sphere:
\[ V = \frac{4}{3} \pi \left( (r_i + t)^3 - r_i^3 \right) \]

For small \( t \) compared to \( r_i \), this can be simplified using a binomial approximation:
\[ V \approx 4 \pi r_i^2 t \]

### Step 4: Mass of Steel
The mass \( M \) of the steel required is then given by the product of the volume and the density of
steel:
\[ M = V \rho \]
\[ M \approx 4 \pi r_i^2 t \rho \]

### Step 5: Substitute Thickness
Substitute the thickness \( t \) from Step 2 into the mass equation:
\[ M \approx 4 \pi r_i^2 \left( \frac{P r_i}{2\sigma} \right) \rho \]
\[ M \approx 2 \pi \frac{P r_i^3 \rho}{\sigma} \]

### Final Formula
The mass of steel required for a hollow sphere to withstand a given external pressure is:
\[ M = 2 \pi \frac{P r_i^3 \rho}{\sigma} \]

### Summary
- \( M \): Mass of steel
- \( P \): External pressure
- \( r_i \): Inner radius of the sphere
- \( \rho \): Density of steel
- \( \sigma \): Allowable stress for the steel

This formula provides the mass of steel dependent on the inner radius of the sphere, given the
external pressure it needs to withstand and the material properties of the steel.
--------------

> 
> (Wie soll das mal im alten Rom gewesen sein? "Hic Rhodos, hic salta!")

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Re: [OT] Wasserstoff (Handelsblatt) Marcel Mueller <news.5.maazl@spamgourmet.org> - 2024-05-23 13:59 +0200
  Re: [OT] Wasserstoff (Handelsblatt) Christoph Müller <chrnewsgroup@astrail.de> - 2024-05-23 21:33 +0200
  Re: [OT] Wasserstoff (Handelsblatt) Sieghard Schicktanz <Sieghard.Schicktanz@SchS.de> - 2024-05-23 21:36 +0200
  Re: [OT] Wasserstoff (Handelsblatt) Hermann Riemann <nospam.ng@hermann-riemann.de> - 2024-05-24 09:49 +0200
    Re: [OT] Wasserstoff (Handelsblatt) Axel Berger <Spam@Berger-Odenthal.De> - 2024-05-24 10:43 +0200
    Re: [OT] Wasserstoff (Handelsblatt) Sieghard Schicktanz <Sieghard.Schicktanz@SchS.de> - 2024-05-25 02:05 +0200
      Re: [OT] Wasserstoff (Handelsblatt) Alexander Schreiber <als@usenet.thangorodrim.de> - 2024-05-25 21:45 +0200
        Re: [OT] Wasserstoff (Handelsblatt) Axel Berger <Spam@Berger-Odenthal.De> - 2024-05-25 22:31 +0200
          Re: [OT] Wasserstoff (Handelsblatt) Marc Haber <mh+usenetspam1118@zugschl.us> - 2024-05-26 07:54 +0200
            Re: [OT] Wasserstoff (Handelsblatt) Axel Berger <Spam@Berger-Odenthal.De> - 2024-05-26 11:15 +0200
              Re: [OT] Wasserstoff (Handelsblatt) Marc Haber <mh+usenetspam1118@zugschl.us> - 2024-05-26 11:34 +0200
              Re: [OT] Wasserstoff (Handelsblatt) Rupert Haselbeck <mein-rest-muell@gmx.de> - 2024-05-26 12:30 +0200
              Re: [OT] Wasserstoff (Handelsblatt) Carla Schneider <carla_schn@proton.me> - 2024-05-26 13:23 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Alexander Schreiber <als@usenet.thangorodrim.de> - 2024-05-26 16:17 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Carla Schneider <carla_schn@proton.me> - 2024-05-27 14:15 +0200
            Re: [OT] Wasserstoff (Handelsblatt) Christoph Müller <chrnewsgroup@astrail.de> - 2024-05-26 12:34 +0200
              Re: [OT] Wasserstoff (Handelsblatt) Carla Schneider <carla_schn@proton.me> - 2024-05-26 13:29 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Christoph Müller <chrnewsgroup@astrail.de> - 2024-05-27 00:11 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Carla Schneider <carla_schn@proton.me> - 2024-05-27 08:13 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Christoph Müller <chrnewsgroup@astrail.de> - 2024-05-27 09:11 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Carla Schneider <carla_schn@proton.me> - 2024-05-27 14:07 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Christoph Müller <chrnewsgroup@astrail.de> - 2024-05-27 16:15 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Carla Schneider <carla_schn@proton.me> - 2024-05-27 18:45 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Christoph Müller <chrnewsgroup@astrail.de> - 2024-05-29 21:07 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Axel Berger <Spam@Berger-Odenthal.De> - 2024-05-29 21:49 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Christoph Müller <chrnewsgroup@astrail.de> - 2024-05-30 08:56 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Sieghard Schicktanz <Sieghard.Schicktanz@SchS.de> - 2024-05-30 21:19 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Christoph Müller <chrnewsgroup@astrail.de> - 2024-05-31 12:30 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Hermann Riemann <nospam.ng@hermann-riemann.de> - 2024-05-31 14:31 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Carla Schneider <carla_schn@proton.me> - 2024-05-31 16:56 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Hermann Riemann <nospam.ng@hermann-riemann.de> - 2024-05-31 17:04 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Carla Schneider <carla_schn@proton.me> - 2024-06-01 14:42 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Alexander Schreiber <als@usenet.thangorodrim.de> - 2024-06-01 16:17 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Christoph Müller <chrnewsgroup@astrail.de> - 2024-05-31 23:03 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Hermann Riemann <nospam.ng@hermann-riemann.de> - 2024-06-01 01:48 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Carla Schneider <carla_schn@proton.me> - 2024-06-01 08:10 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Christoph Müller <chrnewsgroup@astrail.de> - 2024-06-01 20:19 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Sieghard Schicktanz <Sieghard.Schicktanz@SchS.de> - 2024-06-01 01:01 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Sieghard Schicktanz <Sieghard.Schicktanz@SchS.de> - 2024-06-01 00:59 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Christoph Müller <chrnewsgroup@astrail.de> - 2024-06-01 20:28 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Sieghard Schicktanz <Sieghard.Schicktanz@SchS.de> - 2024-06-02 21:49 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Carla Schneider <carla_schn@proton.me> - 2024-05-31 16:52 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Carla Schneider <carla_schn@proton.me> - 2024-05-31 17:05 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Carla Schneider <carla_schn@proton.me> - 2024-05-31 17:44 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Christoph Müller <chrnewsgroup@astrail.de> - 2024-06-01 21:08 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Sieghard Schicktanz <Sieghard.Schicktanz@SchS.de> - 2024-05-27 22:00 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Carla Schneider <carla_schn@proton.me> - 2024-05-28 12:27 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Sieghard Schicktanz <Sieghard.Schicktanz@SchS.de> - 2024-05-28 21:17 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Carla Schneider <carla_schn@proton.me> - 2024-05-29 08:41 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Sieghard Schicktanz <Sieghard.Schicktanz@SchS.de> - 2024-05-30 00:46 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Carla Schneider <carla_schn@proton.me> - 2024-05-31 16:34 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Sieghard Schicktanz <Sieghard.Schicktanz@SchS.de> - 2024-06-01 01:16 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Carla Schneider <carla_schn@proton.me> - 2024-06-03 11:21 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Sieghard Schicktanz <Sieghard.Schicktanz@SchS.de> - 2024-06-03 21:38 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Hermann Riemann <nospam.ng@hermann-riemann.de> - 2024-06-04 05:06 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Carla Schneider <carla_schn@proton.me> - 2024-06-04 11:08 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Sieghard Schicktanz <Sieghard.Schicktanz@SchS.de> - 2024-06-04 21:36 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Stefan <invalid@ignore.invalid> - 2024-06-05 07:08 +0200
                Re: [OT] Wasserstoff (Handelsblatt) Carla Schneider <carla_schn@proton.me> - 2024-06-05 09:39 +0200
            Re: [OT] Wasserstoff (Handelsblatt) Sieghard Schicktanz <Sieghard.Schicktanz@SchS.de> - 2024-05-26 23:19 +0200
        Re: [OT] Wasserstoff (Handelsblatt) Hermann Riemann <nospam.ng@hermann-riemann.de> - 2024-05-26 12:41 +0200
          Re: [OT] Wasserstoff (Handelsblatt) Alexander Schreiber <als@usenet.thangorodrim.de> - 2024-05-26 16:20 +0200
        Re: [OT] Wasserstoff (Handelsblatt) Sieghard Schicktanz <Sieghard.Schicktanz@SchS.de> - 2024-05-26 23:15 +0200
  Re: [OT] Wasserstoff (Handelsblatt) Andreas Bockelmann <xotzil@gmx.de> - 2024-05-24 21:14 +0200
    Re: [OT] Wasserstoff (Handelsblatt) Volker Bartheld <news2024@bartheld.net> - 2024-05-24 21:24 +0200
      Re: [OT] Wasserstoff (Handelsblatt) Axel Berger <Spam@Berger-Odenthal.De> - 2024-05-24 21:40 +0200
        Re: [OT] Wasserstoff (Handelsblatt) Ralph Aichinger <ralph@pi.h5.or.at> - 2024-05-25 05:38 +0000
          Re: [OT] Wasserstoff (Handelsblatt) Andreas Bockelmann <xotzil@gmx.de> - 2024-05-25 08:55 +0200
          Re: [OT] Wasserstoff (Handelsblatt) Heinz Schmitz <sch@example.invalid> - 2024-05-25 10:56 +0200
        Re: [OT] Wasserstoff (Handelsblatt) Hermann Riemann <nospam.ng@hermann-riemann.de> - 2024-05-26 12:47 +0200

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